Question

this table gives a few $(x,y)$ pairs of a line in the coordinate plane.
$x$ $y$
$-94$ $24$
$-74$ $18$
$-54$ $12$
what is the $x$-intercept of the line?
$(square,square)$

Explanation:

Step1: Calculate slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(-94,24)$ and $(x_2,y_2)=(-74,18)$:
$$m=\frac{18-24}{-74-(-94)}=\frac{-6}{20}=-\frac{3}{10}$$

Step2: Find line equation

Use point-slope form $y-y_1=m(x-x_1)$. Substitute $m=-\frac{3}{10}$ and $(x_1,y_1)=(-94,24)$:
$$y-24=-\frac{3}{10}(x+94)$$
Simplify to slope-intercept form $y=mx+b$:
$$y=-\frac{3}{10}x-\frac{3}{10}\times94+24$$
$$y=-\frac{3}{10}x-28.2+24$$
$$y=-\frac{3}{10}x-4.2$$

Step3: Solve for x-intercept

Set $y=0$ and solve for $x$:
$$0=-\frac{3}{10}x-4.2$$
$$\frac{3}{10}x=-4.2$$
$$x=-4.2\times\frac{10}{3}=-14$$

Answer:

$(-14, 0)$