We are given the graph of a line that represents the cost of renting a kayak.
We are asked to find a linear function that represents the relationship of the total cost c of renting a kayak for t hours. The desired linear function has to follow a specific format.
y= m x+ b
In this case, y is represented by c and x is represented by t.
c= m t+ b
For an equation in this form, m is the slope and b is the y-intercept. To find the desired linear function we will calculate the slope and the y-intercept. Let's start by marking two
lattice points on the graph of the line! Recall that a lattice point is a point that lies perfectly on the grid lines.
Now we can use these points to calculate m. We will start by substituting the points into the Slope Formula.
In our function, a slope of 3 means that if we rent a kayak for 1 more hour we will pay $ 3 more. Now that we know the slope, we can write a partial version of the equation.
c= 3 t+ b
To complete the equation, we also need to determine the y-intercept b. Since we know that our points will satisfy the equation, we can substitute one of them into the equation to solve for b. Let's use ( 1, 10).
A y-intercept of 7 means that if we rent a kayak for any number of hours, we will pay $ 7 in advance regardless of the number of hours. We can now complete the equation.
c= 3t+ 7
