# How do you find the slope and y intercept to sketch y=3x -1?

Dec 7, 2015

For the line $y = 3 x - 1$, the slope is $\frac{3}{1}$ and the y-intercept is $\left(0 , - 1\right)$.

#### Explanation:

Slope intercept form $\left(y = m x + b\right)$, is great because we can easily find several clues about the line from its equation.

In slope intercept form, $m =$the slope of the line, and $b =$the y-coordinate of the y-intercept (the point where the line intersects the vertical y-axis).

In this case, $m = 3$, or $\frac{3}{1}$, and $b = \left(- 1\right)$, which equates to the point $\left(0 , - 1\right)$.

To graph this line, plot the y-intercept we just found by going one unit down from the origin along the y-axis. Then use the slope to graph a few more points. The slope is $\frac{3}{1}$, so you can find your next point 3 units up and 1 unit to the right from your y-intercept, or $\left(1 , 2\right)$.

A positive slope means your points will be [numerator of slope] units up and [denominator of slope] units right, OR [numerator of slope] units down and [denominator of slope] units left. These two methods for positive slopes work because a positive divided by a positive is a positive, and a negative divided by a negative is also a positive.

Using this reasoning, we can plot another point in the opposite direction by going 3 units down and 1 unit to the left of the y-intercept, which would be $\left(- 1 , - 4\right)$.

graph{3x-1 [-10, 10, -5, 5]}