SOLUTION: Line l is perpendicular to the graph of 2x + 3y = 5, and has the same x-intercept as the graph of 2x + 3y = 5. Find the standard form of the equation whose graph is l.

Question 1174154: Line l is perpendicular to the graph of 2x + 3y = 5, and has the same x-intercept as the graph of 2x + 3y = 5. Find the standard form of the equation whose graph is l.

Found 3 solutions by ewatrrr, greenestamps, ikleyn:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi, Line l is perpendicular to the graph of 2x + 3y = 5 and has the same x-intercept y = (-2/3)x + 5/3 |perpendicular lines have negative reciprocals for slopes Line I: y = (3/2)x + 5/3 Graph: y = (-2/3)x + 5/3 and y = (3/2)x + 5/3 Note: Line with the negative slopes slants to the Left Wish You the Best in your Studies.

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

The other tutor found an equation of a line perpendicular to the given line and having the same y-intercept -- not the same x-intercept.

The standard form equation of the given line is 2x+3y=5.

Skipping a few steps, the equation of any line perpendicular to the given line is 3x-2y=c for come constant c. (Switch the coefficients of x and y and change the sign of one of them.)

The x-intercept of the given equation, found by setting y=0, is (2.5,0).

Plugging those x and y values in the equation of the line we are looking for gives us

3(2.5)-2(0) = c
c = 7.5

ANSWER: The equation of the line we are looking for is

In slope-intercept form the two equations are y = (-2/3)x+5/3 and y = (3/2)x-3.75. Graphs:

Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.

The solution by @ewatrrr is incorrect.

Follow to correct solution by @greenestamps.

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