Question 1174154
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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.<br>
The standard form equation of the given line is 2x+3y=5.<br>
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.)<br>
The x-intercept of the given equation, found by setting y=0, is (2.5,0).<br>
Plugging those x and y values in the equation of the line we are looking for gives us<br>
3(2.5)-2(0) = c
c = 7.5<br>
ANSWER: The equation of the line we are looking for is<br>
{{{3x-2y = 7.5}}}<br>
In slope-intercept form the two equations are y = (-2/3)x+5/3 and y = (3/2)x-3.75.  Graphs:<br>
{{{graph(200,200,-2,8,-5,5,(-2/3)x+5/3,(3/2)x-3.75)}}}<br>