SOLUTION: The line through (2,-3) that is perpendicular to the line y= -4x + 8 written in standard form containing only integer coefficients. I am having a horrible time with these graphs,

Question 181883: The line through (2,-3) that is perpendicular to the line y= -4x + 8 written in standard form containing only integer coefficients. I am having a horrible time with these graphs, any help is greatly appreciated!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point

.

Start with the point slope formula

Plug in , , and

Rewrite as

Multiply both sides by 4.

Distribute

Subtract 12 from both sides.

Subtract "x" from both sides.

Combine like terms.

Rearrange the terms.

Multiply EVERY term by -1 to make the "x" coefficient positive.

=============================================

Answer:

So the equation of the line that is perpendicular to and goes through the point (2,-3) in standard form is

Here's the graph of the two lines to verify the answer:

Graph of the original equation (red) and the perpendicular line (green) through the point

.

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