In the xy -plane, line p has a slope of - 5 3 and an x -intercept of ( -

Question

In the xy -plane, line p has a slope of - 5 3 and an x -intercept of ( - 6 , 0 ) . What is the y -coordinate of the y -intercept of line p ?

Accepted Answer

The correct answer is - 10 . A line in the xy -plane can be represented by the equation y = m x + b , where m is the slope of the line and b is the y -coordinate of the y -intercept. It's given that line p has a slope of - 5 3 . Therefore, m = - 5 3 . It's also given that line p has an x -intercept of - 6 , 0 . Therefore, when x = - 6 , y = 0 . Substituting - 5 3 for m , - 6 for x , and 0 for y in the equation y = m x + b yields 0 = - 5 3 - 6 + b , which is equivalent to 0 = 10 + b . Subtracting 10 from both sides of this equation yields - 10 = b . Therefore, the y -coordinate of the y -intercept of line p is - 10 .

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