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In the xy-plane, line l has a y-intercep...

In the xy-plane, line l has a y-intercept of −13 and is perpendicular to the line with equationy= − `2/3` x. If the point (10, b) is on line l, what is the value of b ?

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The correct Answer is:
2
It’s given that line l is perpendicular to the line with equation y = − `2/3` x. Since the equation y = − `2/3` x is written in slope-intercept form, the slope of the line is `− 2/3` . The slope of line l must be the negative reciprocal of `− 2/3` , which is `3/2` . It’s also given that the y-coordinate of the y-intercept of line ℓ is −13, so the equation of line l in slope-intercept form is `y=3/2x-13` . If y = b when x = 10, `b=3/2(10)-13`, which is equivalent to b = 15 − 13, or b = 2.
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