In the xy -plane, line l passes through the point 0 , 0 and is parallel to the line represented

Question

In the xy -plane, line l passes through the point 0 , 0 and is parallel to the line represented by the equation y = 8 x + 2 . If line l also passes through the point 3 , d , what is the value of d ?

Accepted Answer

The correct answer is 24 . A line in the xy -plane can be defined 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 of the line. It's given that line l passes through the point 0 , 0 . Therefore, the y -coordinate of the y -intercept of line l is 0 . It's given that line l is parallel to the line represented by the equation y = 8 x + 2 . Since parallel lines have the same slope, it follows that the slope of line l is 8 . Therefore, line l can be defined by an equation in the form y = m x + b , where m = 8 and b = 0 . Substituting 8 for m and 0 for b in y = m x + b yields the equation y = 8 x + 0 , or y = 8 x . If line l passes through the point 3 , d , then when x = 3 , y = d for the equation y = 8 x . Substituting 3 for x and d for y in the equation y = 8 x yields d = 8 3 , or d = 24 .

Question 155657