The question is incomplete. The complete question is here.
A line passes through point (-2, 5) and has a slope of 2/3. Points A(x, 3) and B(-2, y) lie on the line.
The value of x is ___, the value of y is ___.
Answer:
The value of x is -5, and the value of y is 5
Step-by-step explanation:
The form of a linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0), to find b substitute x and y in the equation by the coordinates of a point on the line
∵ The slope of the line is [tex]\frac{2}{3}[/tex]
∴ m = [tex]\frac{2}{3}[/tex]
∵ The form of the equation is y = m x + b
∴ y = [tex]\frac{2}{3}[/tex] x + b
- Substitute x and y by the coordinates of a point on the line
∵ The line passes through point (-2 , 5)
∴ x = -2 and y = 5
∵ 5 = [tex]\frac{2}{3}[/tex] (-2) + b
∴ 5 = [tex]\frac{-4}{3}[/tex] + b
- Add [tex]\frac{-4}{3}[/tex] to both sides
∴ [tex]\frac{19}{3}[/tex] = b
∴ y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{19}{3}[/tex]
∵ Point A (x , 3) lies on the line
- Substitute y by 3 to find x
∴ 3 = [tex]\frac{2}{3}[/tex] x + [tex]\frac{19}{3}[/tex]
- Subtract [tex]\frac{19}{3}[/tex] from both sides
∴ [tex]\frac{-10}{3}[/tex] = [tex]\frac{2}{3}[/tex] x
- Divide both sides by [tex]\frac{2}{3}[/tex]
∴ -5 = x
∴ The value of x = -5
∵ Point B (-2 , y) lies on the line
- Substitute x by -2 to find y
∴ y = [tex]\frac{2}{3}[/tex] (-2) + [tex]\frac{19}{3}[/tex]
∴ y = [tex]\frac{-4}{3}[/tex] + [tex]\frac{19}{3}[/tex]
∴ y = [tex]\frac{15}{3}[/tex]
∴ y = 5
∴ The value of y = 5
