Question

Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9 Find the slope of the line 2x−3y=9. Use a forward slash (i.e. "/") for all fractions (e.g. 1/2 for 12). m=____ What would the parallel slope be? m=______ Use the slope to find the y-intercept of the parallel line. b= _____

Answer 1

Explanation:

2x - 3y = 9

-3y = -2x + 9

`y=(-2)/(-3)x + (9)/(-3)\\\\y=(2)/(3)x-3\\`

Parallel lines have same slope.So,

Slope m = 2/3

(4 , -1)

Equation: y - y1 = m(x - x1)

`y-[-1]=(2)/(3)(x - 4)\\\\y+1=(2)/(3)*x - (2)/(3)*4\\\\y+1=(2)/(3)x-(8)/(3)\\\\y=(2)/(3)x-(8)/(3)-1\\\\y=(2)/(3)x-(8)/(3)-(3)/(3)\\\\y=(2)/(3)x-(11)/(3)`

b = -11/3