SOLUTION: With x-intercept -3/7 and perpendicular to the line defined by the equation 3x+4y=10. Sketch the line

Question 1152574: With x-intercept -3/7 and perpendicular to the line defined by the equation 3x+4y=10. Sketch the line
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
tghe x-intercept is -3/7
the line is perpendicular to the line defined by the equation 3x + 4y = 10
convert that equation to slope intercept form as shown below:
start with 3x + 4y = 10
subtract 3x from both sides of the equation to get:
4y = 10 - 3x
divide both sides of the equation by 4 to and reorder the terms in descending order of degree to get:
y = -3/4 * x + 10/4.
that line is now in the slope intercept form of y = mx + b.
m is the slope and b is the y-intercept.
the line perpendicular to this line will have a slope that is a negative reciprocal to it.
that makes the slope of the perpendicular line equal to 4/3.
the slope intercept form of the equation of that perpendicular line is y = 4/3 * x + b
b is the y-intercept of the line.
if the x-intercept of that line is -3/7, then a point on that line is (-3/7,0).
to find the value of b, replace x with -3/7 and y with 0 to get:
y = 4/3 * x + b becomes 0 = 4/3 * -3/7 + b
4/3 * -3/7 is equal to -12/21.
the equation becomes 0 = -12/21 + b
solve for b to get b = 12/21.
the equation of the line perpendicular to the original line is y = 4/3 * x + 12/21.
here's a graph of both lines.

the red line is the original line.
you can see that it intersects with the y-axis at the point (0,2.5)
that means it's y-intercept is 2.5 which is the same as 10/4.
the blue line is the line that's perpendicular to it.
you can see that the x-intercept of that line is at the point (-.429,0).
-.429 is the decimal form of -3/7 rounded to 3 decimal places.
the y-intercept is the value of x when y = 0.
the x-intercept is the value of y when x = 0.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
With x-intercept -3/7 and perpendicular to the line defined by the equation 3x+4y=10. Sketch the line
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Step 1, find the slope of 3x+4y = 10.
Step 2, find a line whose slope is the negative inverse of the slope of 3x+4y = 10.
Step 3, find an equation of a line with the slope in Step 2 passing thru the point (-3/7,0)
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To sketch it, find a 2nd point and draw a straight line thru (-3/7,0) and the 2nd point.
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