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

0, -26

Explanation:

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Answer 2

The y-intercept is:

`(0,-26)`

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=(-78-(-52))/(68-34)=(-26)/(34)=-(13)/(17)`

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

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