11. David does landscaping for private homes and businesses. He charges $40 to travel to the site and then $40 per hour for his services. The equation y = 40 +40x models the charge for his services y for any number of hours x. a. Graph the equation. b. What is the slope of the line? What does the slope represent? c. What is the y-intercept of the line? What does the y-intercept represent? d. Julia paid David $240 for his services. How many hours did David work?

a. To graph the equation y = 40 + 40x, we can plot points on a coordinate plane. The x-axis represents the number of hours worked (x), and the y-axis represents the charge for David's services (y).

Let's choose a few values for x and calculate the corresponding values for y:

For x = 0, y = 40 + 40(0) = 40. This means that if David doesn't work any hours, he still charges $40 for traveling to the site.

For x = 1, y = 40 + 40(1) = 80. This means that if David works 1 hour, he charges $80 in total.

For x = 2, y = 40 + 40(2) = 120. This means that if David works 2 hours, he charges $120 in total.

We can continue this process to find more points and then plot them on the graph. Once we have enough points, we can connect them with a straight line.

b. The slope of the line is 40. In the equation y = 40 + 40x, the coefficient of x (40) represents the rate at which the charge increases per hour. So, for every additional hour worked, the charge increases by $40.

c. The y-intercept of the line is 40. In the equation y = 40 + 40x, the constant term (40) represents the initial charge for traveling to the site. It is the amount David charges even if he doesn't work any hours.

d. If Julia paid David $240 for his services, we can substitute this value into the equation y = 40 + 40x and solve for x:

240 = 40 + 40x

Subtracting 40 from both sides:

200 = 40x

Dividing both sides by 40:

x = 5

Therefore, David worked for 5 hours to earn $240 for his services.

Learn more about graphing a linear equation here: brainly.com/question/30286770

semsee45 semsee45 · Answer 2 · 2023-12-30T14:58:52+01:00

Answer:

a) See attachment.

b) The slope of the line is 40. This means that for each additional hour worked, the total charge increases by $40.

c) The y-intercept of the line is 40. This represents the cost charged even if no hours are worked (i.e. the cost of the travelling to the site).

d) 5 hours

Step-by-step explanation:

The equation y = 40 + 40x models how much David charges for his landscaping services, where y is the amount charged (in dollars) and x is the number of hours worked.

The given equation is in slope-intercept form:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope-intercept form of a linear equation}}\\\\\large\text{$y=mx+b$}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\;\textsf{$b$ is the $y$-intercept.}\\\end{array}}[/tex]

Slope

The slope is the coefficient of x, so in the case of the equation y = 40 + 40x, the slope of the line is 40.

The slope represents the rate of change of the dependent variable (total charge) with respect to the independent variable (number of hours). So, for each additional hour worked, the total charge increases by $40.

y-intercept

The y-intercept is the constant term, so in the case of the equation y = 40 + 40x, the y-intercept of the line is 40.

The y-intercept represents the initial cost, which is the cost incurred even if no hours are worked. In this scenario, it's the travel charge of $40.

Graphing the equation

To graph the equation, begin by determining an appropriate scale for the axes. Let each unit on the x-axis represent $50 on the y-axis. As David cannot charge a negative amount or work a negative number of hours, both axes will be in the positive direction only. Label the x-axis "Number of hours worked" and label the y-axis "Total charge (in dollars)".

Plot the y-intercept at (0, 40). The slope of 40 means that for each unit increase in x, the value of y increases by 40, so another point on the line is (1, 80). Plot this point, then draw a straight line from (0, 40) through point (1, 80).

Number of hours worked

Given that Julia paid David a total of $240 for his services, then y = 240.

To find the number of hours David worked, substitute y = 240 into the equation and solve for x:

[tex]\begin{aligned}240&=40+40x\\\\240-40&=40+40x-40\\\\200&=40x\\\\\dfrac{200}{40}&=\dfrac{40x}{40}\\\\5&=x\end{aligned}[/tex]

Alternatively, we can use the graph (see attached) to determine the number of hours David worked for a total payment of $240. Locate the point on the graph where y = 240 and find its corresponding x-value, which is x = 5.

Therefore, if Julia paid David $240 for his services, David worked a total of 5 hours.