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Plot the points in a coordinate plane and draw a line through them. Calculate the slope and find the y-intercept of the line.
y=-1/4x
A linear function is a function whose graph is a nonvertical line. The equation of this type of function follows a specific format, called slope-intercept form. y=mx+b Here, m is the slope and b is the y-intercept of the line. With this information in mind, let's consider the given table of values.
| x | - 8 | - 4 | 0 | 4 |
|---|---|---|---|---|
| y | 2 | 1 | 0 | -1 |
Let's find the slope of the line. Recall that the slope m is the ratio of the change in y to the change in x. m=change iny/change inx ⇔ m=y_2-y_1/x_2-x_1 We can use any two points of the line to find the slope. We will arbitrarily use ( 0, 0) and ( 4, -1).
Substitute ( 0,0) & ( 4,-1)
We found that the slope of the line is - 14. Let's write a partial equation for our line. y= -1/4x+b Finally, because the line crosses the y-axis at (0, 0), the y-intercept b is 0. y= -1/4x+ 0 ⇔ y= -1/4x Let's add this information to our diagram.