SOLUTION: Find the equation of the line in standard form that passes through (-7,5) and is perpendicular to -4x+3y=13. So far I have: -4x+4x+3y=4x+13 3y/3=4x/3+13/3 y=4/3x+13/3. Am

Click here to see ALL problems on Linear-systems

Question 572056: Find the equation of the line in standard form that passes through (-7,5) and is perpendicular to -4x+3y=13.
So far I have:
-4x+4x+3y=4x+13
3y/3=4x/3+13/3
y=4/3x+13/3.
Am I right at all? And if so, where do I go from here?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the line is perpendicular to is:
-4x + 3y = 13
you have to put this equation into slope intercept form.
add 4x to both sides of this equation to get:
3y = 4x + 13
divide both sides of this equation by 3 to get:
y = (4/3)x + (13/3)
that gets you the equation of the line that you have to be perpendicular to into slope intercept form.
the general of slope intercept form is:
y = mx + b
m equals the slope.
b equals the y intercept.
the slope of the line formed by this equation is (4/3)
for a line to be perpendicular to it, the slope of that line has to be the negative reciprocal of it.
the negative reciprocal of (4/3) is equal to -(3/4).
that the slope of your new line.
the general form of your new line becomes:
y = -(3/4)x + b
your new line goes through the point (-7,5)
replace x with -7 and y with 5 in the slope intercept form of your new line to get:
5 = -(3/4)(-7) + b
solve for b.
simplify the equation to get:
5 = (21/4) + b
subtract (21/4) from both sides of this equation to get:
5 - (21/4) = b
simplify to get:
-1/4 = b
that's your answer in fraction form.
the equation of the line perpendicular to your original line and passing through the point (-7,5) is:
y = -(3/4)x - (1/4)
let's see if that's true.
the graph of your 2 lines is shown below:

they look perpendicular to each other.
their y intercepts should be:
original equation y intercept = (13/3)
perpendicular equation y intercept = -(1/4)
i placed horizontal lines as y = (13/3) and -(1/4) to see if the y intercepts are correct.
that graph looks like this:

all that's required to see if if the perpendicular line passes through the point (-7,5).
i placed a vertical line at x = -7 and a horizontal line at y = 5 to see if that point is on the perpendicular line.
that graph is shown below:

since the line of the perpendicular equation intersects with the lines x = -7 and y = 5, this means that the point (-7,5) is on the line of the perpendicular equation.
everything check out, so the equation of the line perpendicular to the original line is:
y = -(3/4)x - (1/4)