Answer:
The equation of the line in the slope-intercept form is y = [tex]\frac{4}{3}[/tex] x + 4 ⇒ A
Step-by-step explanation:
The slope-intercept form is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (y at x = 0)
The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ The line passes through points (-6 , -4) and (0 , 4)
∴ [tex]x_{1}[/tex] = -6 and [tex]x_{2}[/tex] = 0
∴ [tex]y_{1}[/tex] = -4 and [tex]y_{2}[/tex] = 4
- Substitute them in the formula of the slope
∴ [tex]m=\frac{4--4}{0--6}=\frac{8}{6}[/tex]
- Simplify it by divide up and down by 2
∴ [tex]m=\frac{4}{3}[/tex]
∵ The slope-intercept form is y = m x + b
- Substitute the value of m on it
∴ y = [tex]\frac{4}{3}[/tex] x + b
∵ b is value y at x= 0
∵ At x = 0 , y = 4 ⇒ given point
∴ b = 4
- Substitute the value of b in the equation
∴ y = [tex]\frac{4}{3}[/tex] x + 4
The equation of the line in the slope-intercept form is y = [tex]\frac{4}{3}[/tex] x + 4
