Question

how do your write the slope intercept form of the equation through: (-3, 1), Paralell to y=-4/3x-1?

Answer 1

Given line y = (-4/3)x-1

Slope of above line  say m1 = -4/3

parallei line has same slope say m2.So required line slope is -4/3

Equation to the through (-3,1) is y-1 = -4/3(x-(-3))

Cross multiplication

(y-1)3 =-4(x+3)

3y-3 = -4x-12

3y+4x-3+12 = 0

4x+3y+9 = 0

Comments

Note :

Slope - intercept - form of a line equation is y = mx + c, where, m is slope and c is y - intercept.

The line equation is (- 4/3)x - 1.

Compare the above equation with slope - intercept - form of a line equation is y = mx + c.

Slope (m) = - 4/3.

Parallel lines have same slopes.

So, The slope of the parallel line is also - 4/3, and the point is (- 3, 1).

Substitute the values of m = - 4/3 and (x, y ) = (- 3, 1) in slope - intercept - form of a line equation : y = mx + c.

1 = (- 4/3)(- 3) + c

1 = 4 + c

⇒ c = 1 - 4 = - 3.

Substitute the values of m = - 4/3 and c = - 3 in slope - intercept - form of a line equation : y = mx + c.

y = (- 4/3)x + (- 3).

Therefore, slope - intercept - form of a line equation through the given point and slope is

y = - (4/3)x - 3.