Consider the following line. y = 7 − 5x Find the change in y for a one-unit change in x. Find the point at which the line crosses the y-axis.
Added by Melissa S.
Step 1
Step 1: Identify the slope of the line from the given equation \( y = 7 - 5x \). Show more…
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Find the slope of each line. See Examples 6 and 7 . $$ x=1 $$
Graphs and Functions
The Slope of a Line
Now we need to determine how much y changes when x changes by 1 unit. The change in y, recall for a line, is given by y = a + bx. We know that the slope is -15, so if x changes by 1 unit, we can find the change in y as follows: change in y = slope * change in x. 15 = change in y * 1 change in y = 15 Take, for example, when x = 1, we have y = 15 - 15(1) = 0. If x increases by 1 unit to x = 2, then y = 15 - 15(2) = -15. Notice that y decreases by 15 units from y = 0. If, instead, x decreases by 1 unit from 1 to x = 0, then y = 15 - 15(0) = 15. Note that in this case, y increases by 15 units from y = 0.
Adi S.
Find the slope and the $y$ -intercept of each line. See Examples 3 through 7. $$ f(x)=\frac{1}{7} x $$
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