x y 18 130 23 160 26 178 For line h , the table shows three values of x and

Question

x y 18 130 23 160 26 178 For line h , the table shows three values of x and their corresponding values of y . Line k is the result of translating line h down 5 units in the xy -plane. What is the x -intercept of line k ?

Accepted Answer

Choice D is correct. The equation of line h can be written in slope-intercept form y = m x + b , where m is the slope of the line and 0 , b is the y -intercept of the line. It&rsquo;s given that line h contains the points 18 , 130 , 23 , 160 , and 26 , 178 . Therefore, its slope m can be found as 160 - 130 23 - 18 , or 6 . Substituting 6 for m in the equation y = m x + b yields y = 6 x + b . Substituting 130 for y and 18 for x in this equation yields 130 = 6 ( 18 ) + b , or 130 = 108 + b . Subtracting 108 from both sides of this equation yields 22 = b . Substituting 22 for b in y = 6 x + b yields y = 6 x + 22 . Since line k is the result of translating line h down 5 units, an equation of line k is y = 6 x + 22 - 5 , or y = 6 x + 17 . Substituting 0 for y in this equation yields 0 = 6 x + 17 . Solving this equation for x yields x = - 17 6 . Therefore, the x -intercept of line k is - 17 6 , 0 . 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.

$x$	$y$
$18$	$130$
$23$	$160$
$26$	$178$

Question x-y-18