Question

this table gives a few (x, y) pairs of a line in the coordinate plane.
what is the x - intercept of the line?
related content
intercepts from a table

Explanation:

Step1: Find the slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-70,-68)$ and $(x_2,y_2)=(-68,-51)$. Then $m=\frac{-51-(-68)}{-68 - (-70)}=\frac{-51 + 68}{-68+70}=\frac{17}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-70,-68)$ and $m = \frac{17}{2}$, we have $y+68=\frac{17}{2}(x + 70)$.

Step3: Find the x - intercept

The x - intercept is the value of $x$ when $y = 0$. Substitute $y = 0$ into the equation $y+68=\frac{17}{2}(x + 70)$. So, $0+68=\frac{17}{2}(x + 70)$. First, simplify the left - hand side: $68=\frac{17}{2}(x + 70)$. Then multiply both sides by $\frac{2}{17}$: $68\times\frac{2}{17}=x + 70$. Since $68\times\frac{2}{17}=8$, we have $8=x + 70$. Solve for $x$: $x=8 - 70=-62$.

Answer:

$(-62,0)$