Question

1. a line passes through the points (3, 6) and (18, 26).

a. write an equation of the line in point - slope form.
b. write an equation of the line in slope - intercept form.

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(3,6)$ and $(x_2,y_2)=(18,26)$:
$m=\frac{26-6}{18-3}=\frac{20}{15}=\frac{4}{3}$

Step2: Write point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use $(3,6)$:
$y-6=\frac{4}{3}(x-3)$
(Note: Using $(18,26)$ gives $y-26=\frac{4}{3}(x-18)$, which is also valid)

Step3: Convert to slope-intercept form

Start with $y-6=\frac{4}{3}(x-3)$. Distribute $\frac{4}{3}$:
$y-6=\frac{4}{3}x - 4$
Add 6 to both sides:
$y=\frac{4}{3}x + 2$

Answer:

a. $y-6=\frac{4}{3}(x-3)$ (or $y-26=\frac{4}{3}(x-18)$)
b. $y=\frac{4}{3}x + 2$