x = 4 is y = 650 & y = 575 for x = 7. The amount owed decreases by -25 per month.
Identify the ordered pairs from the graph. The graph shows two data points:
Point 1: (4, 650)
Point 2: (11, 475)
The slope of the line. The slope represents the change in y (amount owed) per unit change in x (time). We can use the formula:
Slope = (y2 - y1) / (x2 - x1)
Substituting the values from the points, we get:
Slope = (475 - 650) / (11 - 4)
Slope = -175 / 7
Slope = -25
Step 3: Analyze the slope. A negative slope indicates that the line is decreasing, which means the amount owed decreases as time passes. The steeper the slope, the faster the amount owed decreases.
The y-intercept is the point where the line crosses the y-axis (amount owed when time is 0). We can use the point-slope form of the equation:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting the known values, we get:
y = (-25)x + b
For point (4, 650), we can plug in the values to solve for b:
650 = (-25)(4) + b
650 = -100 + b
b = 750
Therefore, the equation of the line is:
y = -25x + 750
Answer the questions.
For x = 4, what is y?
Plugging in x = 4 into the equation, we get:
y = (-25)(4) + 750
y = -100 + 750
y = 650
Therefore, when x = 4, y = 650.
For y = 575, what is x?
Plugging in y = 575 into the equation, we get:
575 = (-25)(x) + 750
575 - 750 = (-25)(x)
- 175 = (-25)(x)
Dividing both sides by 25 we get
-7 = -x
So, x = 7
Therefore, when y = 575, x = 7.