For the first line in the system:

The line slants gradually down from left to right.

The line passes through the following points:

(3 comma 2)

(8 comma 0)

Question

What system of linear equations is represented by the lines shown?

Accepted Answer

Choice D is correct. A line in the xy -plane that passes through the points x 1 , y 1 and x 2 , y 2 has slope m , where m = y 2 - y 1 x 2 - x 1 , and can be defined by an equation of the form y - y 1 = m x - x 1 . One of the lines shown in the graph passes through the points 8 , 0 and 3 , 4 . Substituting 8 for x 1 , 0 for y 1 , 3 for x 2 , and 4 for y 2 in the equation m = y 2 - y 1 x 2 - x 1 yields m = 4 - 0 3 - 8 , or m = - 4 5 . Substituting - 4 5 for m , 8 for x 1 and 0 for y 1 in the equation y - y 1 = m x - x 1 yields y - 0 = - 4 5 x - 8 , which is equivalent to y = - 4 5 x + 32 5 . Adding 4 5 x to both sides of this equation yields 4 5 x + y = 32 5 . Multiplying both sides of this equation by - 10 yields - 8 x - 10 y = - 64 . Therefore, an equation of this line is - 8 x - 10 y = - 64 . Similarly, the other line shown in the graph passes through the points 8 , 0 and 3 , 2 . Substituting 8 for x 1 , 0 for y 1 , 3 for x 2 , and 2 for y 2 in the equation m = y 2 - y 1 x 2 - x 1 yields m = 2 - 0 3 - 8 , or m = - 2 5 . Substituting - 2 5 for m , 8 for x 1 , and 0 for y 1 in the equation y - y 1 = m x - x 1 yields y - 0 = - 2 5 x - 8 , which is equivalent to y = - 2 5 x + 16 5 . Adding 2 5 x to both sides of this equation yields 2 5 x + y = 16 5 . Multiplying both sides of this equation by 10 yields 4 x + 10 y = 32 . Therefore, an equation of this line is 4 x + 10 y = 32 . So, the system of linear equations represented by the lines shown is 4 x + 10 y = 32 and - 8 x - 10 y = - 64 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

Question for-th