Question

what is an equation of the line that passes through the points (2, -5) and (5, -2)?

Explanation:

Step1: Calculate slope of the line

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(2,-5)$ and $(5,-2)$:
$$m=\frac{-2-(-5)}{5-2}=\frac{3}{3}=1$$

Step2: Use point-slope form

Point-slope form: $y-y_1=m(x-x_1)$. Use $(2,-5)$ and $m=1$:
$$y-(-5)=1(x-2)$$

Step3: Simplify to slope-intercept form

Simplify the equation:
$$y+5=x-2$$
$$y=x-7$$

Answer:

$y=x-7$ (or equivalent forms like $x-y-7=0$)