First, use the given points to calculate the slope.
Then, identify the y-intercept.
y=- 5/2x-1
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
- 4
9
- 2
4
0
- 1
2
- 6
Let's now substitute the first two points given in the table, (- 4,9) and (- 2,4), into the Slope Formula and calculate m.
We calculated that the slope of the given equation is - 52, which means that for every 2 horizontal steps in the positive direction, we take 5 vertical steps in the negative direction. Now that we know the slope, we can write a partial version of the equation.
y= - 5/2 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
- 4
9
- 2
4
0
- 1
2
- 6
Since y= - 1 when x=0, the y-intercept is - 1. This means that the line crosses the y-axis at the point (0, - 1). We can now complete the equation.
y= -5/2x+( - 1) ⇔ y=- 5/2x-1
