Model the data in the table with a linear equation in slope-intercept form. Then tell what the slope and y-intercept represent.
Time Worked, x (h) 1 3 6 9
Wages Earned, y ($) 9.00 27.00 54.00 81.00
To model the data in the table with a linear equation in slope-intercept form, we can apply the formula:
y = mx + b
where:
- y is the dependent variable (in this case, Wages Earned)
- x is the independent variable (in this case, Time Worked)
- m is the slope of the line
- b is the y-intercept
To find the linear equation, we can examine the pattern in the data:
Time Worked, x (h) | Wages Earned, y ($)
1 ................................|............... 9.00
3 ................................|............... 27.00
6 ................................|............... 54.00
9 ................................|............... 81.00
We notice that as the time worked (x) increases, the wages earned (y) also increase. Additionally, the wages earned seem to increase at a consistent rate.
To find the linear equation, we can calculate the slope (m) using the first two data points:
m = (change in y) / (change in x)
= (27.00 - 9.00) / (3 - 1)
= 18.00 / 2
= 9.00
Now that we know the slope (m = 9.00), we can find the y-intercept (b) by substituting the values of one of the data points and the slope into the formula:
9.00 = 9.00 * 1 + b
9.00 = 9.00 + b
b = 9.00 - 9.00
b = 0.00
Therefore, the linear equation in slope-intercept form that models the data in the table is:
y = 9.00x + 0.00
The slope (m = 9.00) represents the rate at which the wages earned (y) increase for each additional hour of time worked (x). In this case, the slope indicates that the wages earned increase by $9.00 for each additional hour worked.
The y-intercept (b = 0.00) represents the initial amount of wages earned when no time has been worked. In this case, it indicates that if no time is worked, there are no wages earned.