The equation gives the exact y-value for a certain x-value.
A
About $5.60
B
$5.63
Practice makes perfect
We want to estimate the cost of riding 5.25 miles in a taxi. The cost y of riding in a taxi for x miles is given by a linear equation.
y=0.5x+3
We will create a graph of the equation to make an estimation of the cost. First, we make a table of values. In the table, we will calculate the y-value when x is 1, 2, and 3. This will give us three ordered pairs that satisfy the equation.
x
0.5x+3
y
(x,y)
1
0.5( 1)+3
3.5
( 1, 3.5)
2
0.5( 2)+3
4
( 2, 4)
3
0.5( 3)+3
4.5
( 3, 4.5)
The graph of an equation contains all of the ordered pairs of that equation. This means that all of the ordered pairs are points on the line. We can draw a line that connects the points (1,3.5), (2,4), and (3,4.5) to create our graph.
Now, we can use our graph to estimate the cost y when the number of miles x is 5.25. We will draw a vertical line from x=5 until it hits our graph. From the point where it hits our graph, we will draw a horizontal line to the y-axis. This is the estimated value for the cost.
The red circle is slightly above 5.5, let's say around 5.6. This means that our estimation is that the cost to ride 5.25 miles in a taxi is about $5.60.
Now we want to find the exact cost of riding 5.25 miles in a taxi. We will use the same linear equation as in Part A.
y=0.5x+3
This time, we will directly use the equation to calculate the value of y when x is 5.25. Let's substitute this value of x into the equation.
