The line slants sharply down from left to right.

The line passes through the following points:

(0 comma 6)

(1 comma 3)

Question

The graph shows a linear relationship between $x$ and $y$ . Which equation represents this relationship, where $R$ is a positive constant?

Accepted Answer

Choice C is correct. The equation representing the linear relationship shown can be written in slope-intercept form y = m x + b , where m is the slope and 0 , b is the y -intercept of the line. The line shown passes through the points 0 , 6 and 2 , 0 . Given two points on a line, x 1 , y 1 and x 2 , y 2 , the slope of the line can be calculated using the equation m = y 2 - y 1 x 2 - x 1 . Substituting 0 , 6 and 2 , 0 for x 1 , y 1 and x 2 , y 2 , respectively, in this equation yields m = 0 - 6 2 - 0 , which is equivalent to m = - 6 2 , or m = - 3 . Since 0 , 6 is the y -intercept, it follows that b = 6 . Substituting - 3 for m and 6 for b in the equation y = m x + b yields y = - 3 x + 6 . Adding 3 x to both sides of this equation yields 3 x + y = 6 . Multiplying this equation by 6 yields 18 x + 6 y = 36 . It follows that the equation 18 x + R y = 36 , where R is a positive constant, represents this relationship. Choice A is incorrect. The graph of this relationship passes through the point 0 , 2 , not 0 , 6 . Choice B is incorrect. The graph of this relationship passes through the point 0 , 2 , not 0 , 6 . Choice D is incorrect. The graph of this relationship passes through the point - 2 , 0 , not 2 , 0 .

Question the-li