Question

Write an equation in slope-intercept form of a line with the following characteristics: parallel to the graph of: -4x + 3y= 12 and passes through the origin.

Answer 1

Slope of given line is m=-a/b =4/3

So searched equation is:

y-0=4/3(x-0)
y = 4/3x

Answer 2

The line that's already there: -4x + 3y= 12

Add 4x to each side: 3y = 4x + 12

Divide each side by 3 : y = 4/3 x + 4

The line that's already there has a slope of 4/3.
Any line parallel to it has the same slope but different y-intercept.
If the new line passes through the origin, then its y-intercept is zero.

The equation of the new line is y = 4/3 x