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How to Calculate Y Intercept

Updated March 23, 2017

Y-intercept is a characteristic of linear equation plots that are always straight lines. Linear equations are given in the form: y = axe + b. The letters a and b denote the equation coefficients. Y-intercept is the y-coordinate of the point where the plot crosses the y-axis. Another important characteristic is the plot slope that is numerically equal to the coefficient a. In the steps below, we consider calculation of the y-intercept in two common cases. In the first case, a linear equation is defined with a slope and a point with coordinates x1 and y1. In the second one, the equation is given in the form above, and the coefficients a and b are known.

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  1. Write the linear equation for the point with coordinates x1 and y1:

  2. y1 = ax1 + b

  3. As an example, consider the linear equation plot with the slope 6 that passes through the point having the following coordinates: x1 = 2 and y1 = 7. The equation for this point is:

  4. 7 = 2a + b.

  5. Write the equation for the y-intercept point. Such a point has the coordinate x equals to 0:

  6. y-intercept = 0a + b, or y-intercept = b

  7. Subtract the equation from Step 1 from the equation for the y-intercept point:

  8. y-intercept = b y1 = ax1 + b ------------------- y-intercept - y1 = -ax1.

  9. Then add y1 to both sides of this equation to obtain y-intercept = y1 - ax1 = y1 - (slope * x1). Note that the slope equals to the coefficient a. In our example (see Step 1):

  10. y-intercept = 7 - 6 * 2 = 7 - 12 = -5

  11. Calculate the y-intercept if the coefficients a and b are explicitly defined (the second case). Using the equation from Step 2, you can conclude that the y-intercept equals to the coefficient b:

  12. y-intercept = b

  13. If, for example, the linear equation is given as y = 10x + 3, then the y-intercept is 3.

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