SOLUTION: 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.

Question 175881This question is from textbook
: 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. This question is from textbook

Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: the origin is the point (0,0)

Start with the given equation.

Add to both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

We can see that the equation has a slope and a y-intercept .

Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is .
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point .

Start with the point slope formula

Plug in , , and

Simplify

Distribute

Multiply

Simplify

So the equation of the line parallel to that goes through the point is .

Here's a graph to visually verify our answer:
Graph of the original equation (red) and the parallel line (green) through the point .

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The origin is the point (0,0). This point must
solve the equation
The line given is

I'll put it in slope-intercept form

The general form is
where is the slope, so

Going back to the general form, I can write

To find , plug (0,0) into the general equation

, so the answer is

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