x y k 13 k + 7 - 15 The table gives the coordinates of two points on a line

Question

x y k 13 k + 7 - 15 The table gives the coordinates of two points on a line in the xy -plane. The y -intercept of the line is k - 5 , b , where k and b are constants. What is the value of b ?

Accepted Answer

The correct answer is 33 . It&rsquo;s given in the table that the coordinates of two points on a line in the xy -plane are ( k , 13 ) and ( k + 7 , - 15 ) . The y -intercept is another point on the line. The slope computed using any pair of points from the line will be the same. The slope of a line, m , between any two points, x 1 , y 1 and x 2 , y 2 , on the line can be calculated using the slope formula, m = y 2 - y 1 x 2 - x 1 . It follows that the slope of the line with the given points from the table, ( k , 13 ) and ( k + 7 , - 15 ) , is m = - 15 - 13 k + 7 - k , which is equivalent to m = - 28 7 , or m = - 4 . It's given that the y -intercept of the line is ( k - 5 , b ) . Substituting - 4 for m and the coordinates of the points ( k - 5 , b ) and ( k , 13 ) into the slope formula yields - 4 = 13 - b k - k - 5 , which is equivalent to - 4 = 13 - b k - k + 5 , or - 4 = 13 - b 5 . Multiplying both sides of this equation by 5 yields - 20 = 13 - b . Subtracting 13 from both sides of this equation yields - 33 = - b . Dividing both sides of this equation by - 1 yields b = 33 . Therefore, the value of b is 33 .

$x$	$y$
$k$	$13$
$k plus 7$	$negative 15$

Question 83c4d0