Answer:
The equation of the line is y = [tex]\frac{3}{4}[/tex] x + (-2)
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
- b is the y-intercept ⇒ value of y at x = 0
The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
- (x1, y1) and (x2, y2) are 2 points on the line
From the given figure
∵ The line passes through points (0, -2) and (8, 4)
∴ x1 = 0 and y1 = -2
∴ x2 = 8 and y2 = 4
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{4--2}{8-0}[/tex] = [tex]\frac{4+2}{8}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
∴ m = [tex]\frac{3}{4}[/tex]
→ Substitute it in the form of the equation
∴ y = = [tex]\frac{3}{4}[/tex] x + b
∵ b is the value of y at x = 0
∵ At x = 0, y = -2
∴ b = -2
→ Substitute it in the equation
∴ y = [tex]\frac{3}{4}[/tex] x + (-2)
∴ The equation of the line is y = [tex]\frac{3}{4}[/tex] x + (-2)
