Answer:
The equation of the line is y = [tex]-\frac{11}{2}[/tex] x - 52
Step-by-step explanation:
The form of the linear equation 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 is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ The line passes through the points (-10 , 3) and (-8 , 8)
∴ [tex]x_{1}[/tex] = -10 and [tex]x_{2}[/tex] = -8
∴ [tex]y_{1}[/tex] = 3 and [tex]y_{2}[/tex] = -8
- Substitute them in the formula of the slope
∴ [tex]m=\frac{-8-3}{-8--10}=\frac{-11}{2}[/tex]
∴ m = [tex]-\frac{11}{2}[/tex]
∵ The form of the equation is y = m x + b
∴ y = [tex]-\frac{11}{2}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ x = -8 and y = -8
∴ -8 = [tex]-\frac{11}{2}[/tex] (-8) + b
∴ -8 = 44 + b
- Subtract 44 from both sides
∴ -52 = b
∴ y = [tex]-\frac{11}{2}[/tex] x + (-52)
∴ y = [tex]-\frac{11}{2}[/tex] x - 52
The equation of the line is y = [tex]-\frac{11}{2}[/tex] x - 52
