Question

Passing through the points (6,8) & (9,6)

Answer 1

Slope-intercept form:  y = mx + b  [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]

To find the slope, use the slope formula (m):

$m=\frac{y_2-y_1}{x_2-x_1}$       and plug in the two points

(6, 8) = (x₁, y₁)

(9, 6) = (x₂, y₂)

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

$m=\frac{6-8}{9-6}$

$m=\frac{-2}{3}$      Now that you found the slope, plug it into the equation

y = mx + b

$y=-\frac{2}{3} x+b$       To find b, plug in one of the points, I will use (6, 8)

$8=-\frac{2}{3} (6)+b$

8 = -4 + b    Add 4 on both sides

12 = b         Now plug in b into the equation

$y=-\frac{2}{3} x+12$