What is the slope of the line with equation 3x + 2y = 8?
In order to find the slope, it is simplest to put this line equation into slope-intercept form. If I rearrange this line to be in the form “y = mx + b”, it will be easy to read off the slope m. So I’ll solve: Copyright Elizabeth Stapel 1999-2009 All Rights Reserved 3x + 2y = 8 2y = 3x + 8 y = ( 3/2 ) x + 4 Then the slope is m = 3/2 . Warning: There are many contexts, such as graphing and systems of equations, in which you will need to be able to solve a linear equation for “y =”, so make sure you are comfortable with these techniques. • Find the slope and y-intercept of the line with equation 2x y = 5. I’ll solve for “y =”: 2x y = 5 2x = y + 5 2x 5 = y Then y = 2x 5, and, from the slope-intercept form of y = mx + b, I can see that: the slope is m = 2 and the y-intercept is b = 5. • Find the slope and y-intercept of the line with equation x 2y = 5. I’ll solve for “y =”: x 2y = 5 x = 2y + 5 x 5 = 2y ( 1/2 ) x ( 5/2 ) = y Then y = ( 1/2 ) x ( 5/2 ), so: the slope is m = 1/2 and the y-inte
