The line slants gradually down from left to right.

The line passes through the following points:

(0 comma 7)

(8 comma 0)

Question

The point with coordinates $left parenthesis d comma 4 right parenthesis$ lies on the line shown. What is the value of $d$ ?

Accepted Answer

Choice C is correct. It's given from the graph that the points 0 , 7 and 8 , 0 lie on the line. For two points on a line, x 1 , y 1 and x 2 , y 2 , the slope of the line can be calculated using the slope formula m = y 2 - y 1 x 2 - x 1 . Substituting 0 , 7 for x 1 , y 1 and 8 , 0 for x 2 , y 2 in this formula, the slope of the line can be calculated as m = 0 - 7 8 - 0 , or m = - 7 8 . It's also given that the point d , 4 lies on the line. Substituting d , 4 for x 1 , y 1 , 8 , 0 for x 2 , y 2 , and - 7 8 for m in the slope formula yields - 7 8 = 0 - 4 8 - d , or - 7 8 = - 4 8 - d . Multiplying both sides of this equation by 8 - d yields - 7 8 8 - d = - 4 . Expanding the left-hand side of this equation yields - 7 + 7 8 d = - 4 . Adding 7 to both sides of this equation yields 7 8 d = 3 . Multiplying both sides of this equation by 8 7 yields d = 24 7 . Thus, the value of d is 24 7 . Choice A is incorrect. This is the value of y when x = 4 . Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question 2af9fd