An increasing (or decreasing?) line

Geometry Level 1

The graph of the line y = a x + b y=ax+b passes through the point ( 2 , 90 ) (2, 90) . Additionally, traveling along the line, if x x decreases by 2 2 , then y y decreases by 4 4 . What is the sum of the x x -intercept and the y y -intercept?


The answer is 43.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Andrew Ellinor
Oct 14, 2015

We're told that if x x decreases by 2, then y y decreases by 4. In terms of slope, this means m = Δ y Δ x = 4 2 = 2 m = \frac{\Delta y}{\Delta x} = \frac{-4}{-2} = 2 .

We're also told that the line passes through ( 2 , 90 ) (2, 90) , so we can use point-slope form to find the equation of the line:

y 90 = 2 ( x 2 ) y = 2 x + 86 y - 90 = 2(x - 2) \longrightarrow y = 2x + 86

The y y -intercept is 86 and the x x -intercept is -43, the sum of which is 43.

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...