How To Find Y Intercept With Slope And Point

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The y-intercept of an equation is a point where the graph of the equation intersects the Y-centrality.^[i] There are several ways to find the y-intercept of an equation, depending on the starting information y'all have.

1. 1

   Write downwards the slope and signal. ^[two] The slope or "rise over run" is a single number that tells you lot how steep the line is. This type of problem likewise gives y'all the (10,y) coordinate of ane point forth the graph. Skip to the other methods beneath if you don't take both these pieces of information.

   • Case 1: A straight line with slope two contains the indicate (-three,4). Find the y-intercept of this line using the steps below.

2. 2

   Learn the slope-intercept class of an equation. Any directly line tin be written equally an equation in the form y = mx + b. When the equation is in this form, the variable g is the slope, and b is the y-intercept.

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3. 3

   Substitute the slope in this equation. Write the slope-intercept equation, but instead of m, use the slope of your line.

   • Example i (cont.): y = mx + b
     k = slope = 2
     y = ii10 + b

4. 4

   Replace x and y with the coordinates of the signal. Any time you have the coordinates of a single point on your line, yous can substitute those x and y coordinates for the ten and y in your line equation. Practice this for the equation y'all've been working on.

   • Example i (cont.): The point (3,4) is on this line. At this point, ten = iii and y = 4.
     Substitute these values into y = 2ten +b:
     four = 2(3) + b

5. 5

   Solve for b. Remember, b is the y-intercept of the line. Now that b is the only variable in the equation, rearrange to solve for this variable and observe the answer.

   • Case ane (cont.): iv = ii(3) + b
     iv = 6 + b
     4 - 6 = b
     -2 = b
     The y-intercept of this line is -2.

6. 6

   Write this equally a coordinate point. The y-intercept is the bespeak where the line intersects with the y-axis. Since the y-axis is located at 10 = 0, the x coordinate of the y-intercept is always 0.

   • Example 1 (cont.): The y-intercept is at y = -2, so the coordinate betoken is (0, -2).

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1. 1

   Write down the coordinates of both points. ^[3] This method covers problems that only tell you lot two points on a straight line.^[4] Write each point coordinate down in (x,y) form.

   • Example 2: A straight line passes through points (-1, 2) and (3, -4). Detect the y-intercept of this line using the steps below.

2. ii

   Calculate the ascension and run. Slope is a measure of how much vertical distance the line moves for each unit of horizontal distance. You may take heard this described equally "rise over run" ( ${\displaystyle {\frac {rise}{run}}}$ ).^[5] Hither's how to find these 2 quantities from two points:

   • "Rise" is the change in vertical altitude, or the divergence betwixt the y-values of the two points.
   • "Run" is the change in horizontal distance, or the difference between x-values of the same two points.
   • Example two (cont.): The y-values of the ii points are 2 and -4, then the rise is (-4) - (2) = -half dozen.
     The 10-values of the 2 points (in the aforementioned order) are 1 and 3, then the run is 3 - 1 = two.

3. 3

   Dissever ascension by run to find the slope. Now that you know these two values, plug them into " ${\displaystyle {\frac {rise}{run}}}$ " to find the slope of the line.

   • Example 2 (cont.): ${\displaystyle slope={\frac {rise}{run}}={\frac {-half dozen}{2}}=}$ -three.

4. 4

   Review the slope-intercept form. You can describe a straight line with the formula y = mx + b, where m is the gradient and b is the y-intercept.^[6] Now that we know the slope thousand and a point (x,y), we tin can utilise this equation to solve for b, the y-intercept.

5. five

   Fit the gradient and signal into the equation. Take the equation in slope-intercept class and replace one thousand with the slope you lot calculated. Replace the ten and y terms with the coordinates of a single point on the line.^[7] It doesn't matter which indicate you utilise.

   • Example 2 (cont.): y = mx + b
     Gradient = 1000 = -3, so y = -3x + b
     The line includes a point with (x,y) coordinates (1,two), so two = -3(i) + b.

6. half dozen

   Solve for b. Now the only variable left in the equation is b, the y-intercept. Rearrange the equation so b is on one side, and you accept your reply.^[eight] Call back, the y-intercept e'er has an x-coordinate of 0.

   • Instance two (cont.): ii = -3(1) + b
     2 = -three + b
     5 = b
     The y-intercept is at (0,5).

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1. ane

   Write downwardly the equation of the line. If you already take the equation of the line, you tin can observe the y-intercept with a little algebra.^[ix]

   • Instance iii: What is the y-intercept of the line x + 4y = 16?
   • Note: Example iii is a straight line. Come across the end of this section for an case of a quadratic equation (with a variable raised to the power of two).

2. 2

   Substitute 0 for x. The y-axis is a vertical line along ten = 0. This means any signal on the y-axis has an x-coordinate of 0, including the y-intercept of the line. Plug in 0 for x in the line equation.

   • Example three (cont.): 10 + 4y = 16
     10 = 0
     0 + 4y = sixteen
     4y = 16

3. iii

   Solve for y. The answer is the y-intercept of the line.

   • Example three (cont.): 4y = sixteen
     ${\displaystyle {\frac {4y}{4}}={\frac {16}{4}}}$
     y = 4.
     The y-intercept of the line is four.

4. four

   Confirm past graphing (optional) . To check your respond, graph the equation as neatly as yous can. The point where the line crosses the y-axis is the y-intercept.

5. v

   Notice the y-intercept for a quadratic equation. A quadratic equation includes a variable (10 or y) raised to the power of 2. You can solve for y with the same substitution, but since the quadratic describes a curve, it could intercept the y-axis at 0, 1, or 2 points. This means you may end upwards with 0, i, or 2 answers.

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Add New Question

• Question

  If I take (iii, -12) as my points and an ten-intercept of one, what would the y-intercept exist?

  

  Solve past using Method 2 above. You demand ii points to utilise that method. One point is given every bit (three,-12). The second point is the given x-intercept, which is (1,0).

• Question

  If I am only given one specific point, how tin I convert it into slope intercept grade?

  

  Technist

  Customs Answer

  You can't have only ane point. Imagine you're standing in the middle of your neighborhood street and have no where to go. No direction, no distance, etc. Y'all don't demand to become to your friend's business firm or to school. That is an example of having only ane betoken without any other bespeak to become to and then there'southward no line. Thus, no equation. And more importantly, no math to work out.

• Question

  I practise not become the last part of method 2, tin you explicate?

  

  Using the "gradient-intercept" form of the line'south equation (y = mx + b), you solve for b (which is the y-intercept you're looking for). Substitute the known slope for thou, and substitute the known point's coordinates for ten and y, respectively, in the slope-intercept equation. That volition let you detect b. In the instance in Method two, the calculated gradient is -iii, and then m becomes -3. The known indicate is given as (one,2), so x in the equation becomes 1, and y becomes 2. Thus, the slope-intercept equation becomes two = -three(1) + b. Then 2 = -3 + b, and b = 5. That's the y-intercept.

• Question

  What practise I practice if the only matter on the other side of the = is a variable?

  

  If you hateful that the only affair on the "x" side of the equation is x (so that y = x), that indicates a slope (m) of 1 and a y-intercept (b) of aught.

• Question

  How do I find the y intercept when it is non numbered and obviously a decimal?

  

  Assuming past numbered you hateful whole number, it doesn't matter, the method is the same in both cases.

• Question

  How practise I detect the y-intercept if 3x - y = six?

  

  The graph crosses the y-axis when 10=0, so substitute 0 for x in this equation, and solve for y: y is -six. Since y is -six when x is 0, the y-intercept is -6.

• Question

  How practise I find the y-intercept if the only given information is the slope and no graph or point(s) specified?

  

  You would take to be given more information than just the slope in order to find the y-intercept.

• Question

  How do I find the slope for this and and then the y-intercept (0,0) and (4,-3)?

  

  The slope has a numerator consisting of the departure betwixt any two x values on the line and a denominator consisting of the difference between the 2 respective y values. In this example the slope is (4 - 0) / (-3 - 0), or 4 / -3, which equals -four/3. The y-intercept is the y-value when x=0. In this case, we are told that the line passes through the signal (0,0), which ways that the y-intercept is nothing.

• Question

  What if the slope is undefined?

  

  If a slope is said to be "undefined," that ways that the slope is infinite, which in turn ways that the line is vertical (or parallel to the y-axis).

• Question

  Where is the y-axis on the Cartesian plane?

  

  The y-axis is the vertical line that passes through the origin. Information technology is the series of all points where x = 0.

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• For more than complicated equations, endeavour to isolate the terms containing y onto one side of the equation.

• Some countries utilize a c or another variable instead of b in the equation y = mx + b.^[10] This doesn't change the significant; it's just a different tradition.

• When computing slope betwixt two points, you can subtract the x and y coordinates from each other in either club, as long every bit you put the points in the same order for both rise and run.^[11] For instance, the slope between (i, 12) and (3, vii) tin exist calculated in ii unlike ways:

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Article Summary 10

To discover the y intercept using the equation of the line, plug in 0 for the x variable and solve for y. If the equation is written in the slope-intercept form, plug in the slope and the x and y coordinates for a signal on the line to solve for y. If you don't know the gradient, calculate information technology by dividing the rise of the line past the run. If you want to find the y-intercept if you merely know two points along the line, go on reading the commodity!

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