SOLUTION: Can you help? Determine the equation of a line, instandard form,that has the same x-intercept as 5x+4y-20=0 and is perpendicular to the line 4x+3y-12=0 Thank you for your help.

Algebra ->  Linear-equations -> SOLUTION: Can you help? Determine the equation of a line, instandard form,that has the same x-intercept as 5x+4y-20=0 and is perpendicular to the line 4x+3y-12=0 Thank you for your help.      Log On


   

Question 129738: Can you help?
Determine the equation of a line, instandard form,that has the same x-intercept as 5x+4y-20=0 and is perpendicular to the line 4x+3y-12=0
Thank you for your help.
Found 2 solutions by solver91311, edjones:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The x-intercept of a linear equation in two variables is that point where the line crosses the x-axis, i.e. the point that has a y-coordinate of 0. So, substitute 0 for y and solve for x.

5x%2B4%280%29-20=0
5x=20
x=4

So the x-intercept is (4,0).

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other, that is m%5B1%5D=-1%2Fm%5B2%5D.

So, we need to find the slope of 4x%2B3y-12=0. Put it into slope-intercept form by solving for y:

4x%2B3y-12=0
3y=-4x%2B12
y=-4x%2F3%2B4

That gives us a slope of -4%2F3. Any line perpendicular to this line must have a slope that is the negative reciprocal of -4%2F3, namely 3%2F4.

Now that we have identified the slope of the desired line and a point through which it must pass, we can use the point-slope form of the line to derive the required equation. The point-slope form of the line is y-y%5B1%5D=m%28x-x%5B1%5D%29 where x%5B1%5D and y%5B1%5D are the coordinates of the given point and m is the slope.

y-0=%283%2F4%29%28x-4%29
y=3x%2F4-3

Or, in standard form:
3x-4y=12

Check:
The red line is the derived equation, the green one is the perpendicular and the blue one has the common x-intercept.



Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
5x+4y-20=0
5x+4y=20
x intercept occurs when y=0
5x=20
x=4
4 is the x intercept.
.
4x+3y-12=0
3y=12-4x
y=4-4x/3
-4/3 is the slope of the line.
The slope of a line that is perpendicular is the negative reciprocal of the slope which in this case is 3/4
.
Point slope form:
line passes through the point (x[1],y[1]) and has a slope m
(x,y)=(4,0)
m=3/4
y-y[1]=m(x-x[1])
y-0=(3/4)(x-4)
y=3x/4 - 12/4
y=.75x-3
General form:
3x/4 - y - 3 =0
3x-4y-12=0 multiply each side by 4.
.
Ed
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C4-%284x%2F3%29%2C.75x-3%29