Question

this table gives a few (x,y) pairs of a line in the coordinate plane. x y -79 -68 -68 -51 -57 -34 what is the x - intercept of the line?

Explanation:

Step1: Find the slope of the line

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-79,-68)$ and $(x_2,y_2)=(-68,-51)$. Then $m=\frac{-51-(-68)}{-68 - (-79)}=\frac{-51 + 68}{-68+79}=\frac{17}{11}$.

Step2: Use the point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-79,-68)$ and $m = \frac{17}{11}$, we have $y+68=\frac{17}{11}(x + 79)$.

Step3: Find the x - intercept

The x - intercept is the value of $x$ when $y = 0$. Substitute $y = 0$ into the equation $y+68=\frac{17}{11}(x + 79)$:
$0+68=\frac{17}{11}(x + 79)$
First, multiply both sides by $\frac{11}{17}$: $\frac{11}{17}\times68=x + 79$.
Since $\frac{11}{17}\times68 = 44$, we have $44=x + 79$.
Then solve for $x$: $x=44 - 79=-35$.

Answer:

$-35$