Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in​ slope-intercept form, if possible. (-4,2); 3x-2y=-5

Answer 1

Parallel lines have the SAME slope.

You need to know the slope of the 1st line to find the equation of the 2nd line using the

POINT-SLOPE formula, y - y₁ = m(x - x₁)

(1) Rewrite the 1st equation into the slope-intercept form

3x - 2y = 5..........be the 3x to the LHS

-2y = -3x + 5......divide both sides by -2 to isolate the y on the LHS

y =(^-3/_-2)x + (⁵/_-2)

y =(³/₂)x - ⁵/₂

The slope of the 1st line is ³/₂

Since you have the slope of the 1st line, you know that parallel lines have the same slope, and you have a point on the 2nd line (- 4, 2)...plug the values into the POINT-SLOPE formula,

y - y₁ = m(x - x₁)

y - 2 = (³/₂)(x - (-4))

y - 2 = (³/₂)x + (³/₂)(4)..................... (³/₂)(4), this reduces to 12/2 = 6

y - 2 = (³/₂)x + 6............................... bring the 2 over from the LHS to isolate the y term

y = (³/₂)x + 8 Final Answer

Hope this helps...