Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Pick two points on line

Use $(2, 2)$ and $(3, 7)$

Step3: Calculate the slope

$m = \frac{7 - 2}{3 - 2} = \frac{5}{1} = 5$

Step4: Find y-intercept $b$

Substitute $x=2, y=2, m=5$ into $y=mx+b$:
$2 = 5(2) + b$
$2 = 10 + b$
$b = 2 - 10 = -8$

Step5: Write slope-intercept form

Substitute $m=5, b=-8$ into $y=mx+b$

Answer:

$y = 5x - 8$