# How do you graph y=-4/3x+1 using the slope and intercept?

Dec 28, 2017

See explanation.

#### Explanation:

The line is given in slope-intercept form, $y = m x + b$, where $m$ is the slope and $b$ is the $y$-coordinate of the $y$-intercept, $\left(0 , b\right)$.

By inspection, we can see that the $y$-intercept is $\left(0 , 1\right)$.

The slope is $- \frac{4}{3}$, which we can think of as $\frac{\Delta y}{\Delta x}$ or change in $y$ over change in $x$. I think of it, in this case, as every move of 3 units to the right requires a move of 4 units down to stay on the line. So with that idea in mind, 3 units to the right from the $y$-intercept takes us to $x = 3$. The corresponding 4 units down takes us to $y = 1 - 4 = - 3$. So a second point on the line is $\left(3 , - 3\right)$.

Plot the points $\left(0 , 1\right)$ and $\left(3 , - 3\right)$ and connect them with a straight line.