The graph shows a. The unit rate is $15 per month. The equation of the line is y=15.
The unit rate is the rate of change of the dependent variable (y-axis) with respect to the independent variable (x-axis).
In the case of Miguel's savings graph, the unit rate is the amount of money Miguel saves each month.
To find the unit rate, we can use the slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
where:
m is the slope (unit rate)
(y₁, x₁) and (y₂, x₂) are the coordinates of two points on the line
From the graph, we can choose two points, such as (1, 15) and (4, 60). Substituting these points into the formula, we get:
m = (60 - 15)/(4 - 1) = 45/3 = 15
Therefore, the unit rate is $15 per month. This means that Miguel saves $15 for every month that passes.
The equation of the line can be written in slope-intercept form:
y = mx + b
where:
m is the slope (unit rate)
b is the y-intercept (the point where the line crosses the y-axis)
Using the point (1, 15) and the slope (15), we can solve for the y-intercept:
15 = 15(1) + b
15 = 15 + b
b = 0
Therefore, the equation of the line is:
y = 15x + 0
y = 15x
This confirms that Miguel saves $15 for every month that passes.