Question

This table gives a few (x,y) pairs of a line in the coordinate plane. х y 34 -52 51 -65 68 -78 What is the y-intercept of the line?

Answer 1

ANSWER:

The y-intercept is:

$(0,-26)$

STEP-BY-STEP EXPLANATION:

We have to calculate the equation in its slope-intercept form, which is the following

$\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}$

we calculate the slope with the following formula:

$m=\frac{y_2-y_1}{x_2-x_1_{}}$

we replace the points (34, -52) and (68, -78)

$m=\frac{-78-(-52)}{68-34}=\frac{-26}{34}=-\frac{13}{17}$

now, for b, with the point (51, -65)

$\begin{gathered} -65=-\frac{13}{17}\cdot51+b \\ -65=-39+b \\ b=-65+39 \\ b=-26 \\ \text{Therefore, y-intercept is} \\ (0,-26) \end{gathered}$