The general form of a line containing the point P(-2,1) and with y-intercepts four-fifths the slope.

Question

Please show the complete solution,

Answer 1

If the slope is m and the y-intercept is 4/5 of the slope

then the y-intercept is 4m/5

 

We have two points:  (-2, 1), (0, 4m/5)

 

To find the slope:  m = (change in y)/(change in x)

 

m = (4m/5-1)/(0-(-2))

m = (4m/5 -1)/2

2m = 4m/5 - 1

10m = 4m - 5

6m = -5

m = -5/6

 

We now can use the point slope formula to find the equation of the line

having point (-2, 1) and slope m = -5/6

y - y₁ = m(x-x₁)

y - 1 = (-5/6)(x+2)

6y-6 = -5(x+2)

6y-6 = -5x - 10

5x + 6y - 6 = -10

5x + 6y = -4