A graph has month on the x-axis and saved (money) on the y-axis. Points are at (0, 3,000), (2, 2,450), and (5, 1,625).
The instructor’s friend also plans to rent an apartment in the same complex. Use the graph to identify the y-intercept and the slope used to write the equation in slope intercept form.
y-intercept =
Slope =
Linear equation =
The y-intercept is the value of y when x is equal to 0. From the graph, we can see that at x = 0, the y-value or saved money is 3,000. Therefore, the y-intercept is 3,000.
To find the slope, we can use the formula:
Slope = (change in y) / (change in x)
Using the points (0, 3,000) and (2, 2,450), we can calculate the change in y and change in x:
Change in y = 2,450 - 3,000 = -550
Change in x = 2 - 0 = 2
Therefore, the slope is:
Slope = -550 / 2 = -275
Finally, using the y-intercept and slope, we can write the linear equation in slope-intercept form:
Linear equation = y = slope * x + y-intercept = -275 * x + 3,000
To find the y-intercept and slope, we can use two of the given points on the graph: (0, 3,000) and (2, 2,450).
The y-intercept is the point where the line intersects the y-axis. In other words, it is the value of y when x = 0. From the given points, we can see that when x = 0, y = 3,000. Therefore, the y-intercept is 3,000.
Now, let's find the slope. The slope is a measure of how steep the line is. It indicates the amount by which y changes for each corresponding change in x. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
Using the two points (0, 3,000) and (2, 2,450), the change in y is 2,450 - 3,000 = -550, and the change in x is 2 - 0 = 2. Therefore, the slope is:
slope = -550 / 2 = -275
Now that we have the y-intercept (3,000) and the slope (-275), we can write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
The linear equation is:
y = -275x + 3,000