Answer:
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
