Write an equation for the perpendicular line to the line whose equation is 4y-5x=20 that contains the point (-2,-3)

The equation of a parallel line in point-slope form would be y = -4/5x - 23/5

Step-by-step explanation:

To find this, we must first find the slope of the original line. We can do this by solving for y.

4y - 5x = 20

4y = 5x + 20

y = 5/4x + 5

Now that we have the slope of the original line, we can find the slope of the new line. Perpendicular lines have opposite and reciprocal slopes, which means that while the original slope was 5/4, the new one will be -4/5. Now that we have that, we can use the point and slope and put them into the base form of point-slope form. Then we solve for y to get the final result.

y - y1 = m(x - x1)

y + 3 = -4/5(x + 2)

y + 3 = -4/5x - 8/5

y = -4/5x - 23/5

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

∠cbe and ∠deb are same-side interior angles.

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