Question

what is an equation of the line that passes through the points (6, -1) and (1, 4)?

Explanation:

Step1: Calculate slope $m$

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 $(6,-1)$ and $(1,4)$:
$m=\frac{4-(-1)}{1-6}=\frac{5}{-5}=-1$

Step2: Use point-slope form

Point-slope form: $y-y_1=m(x-x_1)$. Use $(1,4)$:
$y-4=-1(x-1)$

Step3: Simplify to slope-intercept form

Expand and rearrange:
$y-4=-x+1$
$y=-x+5$

Answer:

$y = -x + 5$ (or equivalent forms like $x + y = 5$)