Find the equation of the line that contains the point P(−2, 3) and is perpendicular to the graph of 2x + 4y = −3. I keep getting y=-3x+9?

The line perpendicular to ax+by=c through a given point (x₀,y₀) is bx-ay=bx₀-ay₀.

Here this is 4x - 2y = 4*-2 - 2*3, which simplifies to 2x - y = -7.

Note: If you are not told what form of the linear equation to use in your answer, but one or more forms are used in the question, then use one of those.

Graph: https://www.desmos.com/calculator/e5vanltxvy

4y = - 2x - 3

y= (-1/2) x - 3/4

m1 = - 1/2

m2= 2

y - 3= 2 [ x + 2 ]

y = 2x + 7

Slope of: 2x + 4y = -3 ---> -2/4 = -1/2.

So, the slope of the perpendicular line equals 2.

Equation of the line (with slope = 2, and passing through P (-2,3)):

y - 3 = 2[x - (-2)].

y - 3 = 2(x + 2).

y - 3 = 2x + 4.

y = 2x + 4 + 3.

y = 2x + 7.

Answer: y = 2x + 7.