Consider the point at which the line crosses the x-axis.
A
y=- 5x+25
B
See solution.
Practice makes perfect
We are given a line that shows the amount of money in Amy's bank account.
We want to find the correct equation for the line in slope-intercept form.
This means that the desired equation has to follow a specific format.
y= m x+ b
For an equation in this form, m is the slope and b is the y-intercept. To find the desired equation we will calculate the slope and the y-intercept. Note that we already have two points marked on the line.
We can use these points to calculate m. We will start by substituting the points into the Slope Formula.
Now that we know the slope, we can write a partial version of the equation.
y= - 5 x+ b
To complete the equation, we also need to determine the y-intercept b. Since the line crosses the y-axis at the point (0, 25), the y-intercept is 25. We can now complete the equation.
y= - 5 x+ 25
We want to determine what mistake Amy might have made. Recall the equation that Amy wrote for the line in slope-intercept form.
y=- 5x+ 5
In Part A, we obtained the following equation.
y=- 5x+ 25
We can see that Amy wrote the equation with the wrong y-intercept. She obtained that the y-intercept is equal to 5. To determine what Amy's mistake was, let's consider the graph of the line.
Note that the line crosses the x-axis at the point ( 5,0). Probably Amy's mistake was that she used this point to get the y-intercept.
