First, use the given points to calculate the slope.
Then, identify the y-intercept.
y=1/3x-3
Practice makes perfect
An equation in slope-intercept form follows a specific format.
y= mx+ b
For an equation in this form, m is the slope and b is the y-intercept. We will start by looking at the given table.
x
y
- 3
- 4
0
- 3
3
- 2
6
- 1
Let's now substitute the first two points given in the table, (- 3,- 4) and (0,- 3), into the Slope Formula and calculate m.
We calculated that the slope of the given equation is 13, which means that for every 3 horizontal steps in the positive direction, we take 1 vertical step in the positive direction. Now that we know the slope, we can write a partial version of the equation.
y= 1/3 x+ b
To complete the equation, we also need to determine the y-intercept b. We can consider the given table and find the value of y when x=0.
x
y
- 3
- 4
0
- 3
3
- 2
6
- 1
Since y= - 3 when x=0, the y-intercept is - 3. This means that the line crosses the y-axis at the point (0, - 3). We can now complete the equation.
y= 1/3x+( - 3) ⇔ y=1/3x-3
