Question

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

Answer 1

For the line `y = 3x - 1`, the slope is `3/1` and the y-intercept is `(0, -1)`.

Explanation:

Slope intercept form `(y = mx + b)`, 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 `3/1`, and `b = (-1)`, which equates to the point `(0, -1)`.

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 `3/1`, so you can find your next point 3 units up and 1 unit to the right from your y-intercept, or `(1, 2)`.

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 `(-1, -4)`.

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