Question

owen stops at a gas station. he pays for gas and a car wash. the table shows the total cost, y, as a function of the number of gallons of gas, x.
the initial value is 10. it represents the cost of the car wash.
the rate of change is 4. it represents the cost of each gallon of gas.
write an equation to represent the total cost, y.
y = 4 x + 10
each pair of values in the table should be a solution to y = 4x + 10.
number of gallons, x\ttotal cost ($), y
0\t10
3\t22
6\t34
substitute (3,22) into the equation.
y = 4x + 10

Explanation:

Step1: Identify slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Determine values of m and b

Given rate of change $m = 4$ (cost per gallon of gas) and initial value $b = 10$ (cost of car - wash), so the equation is $y=4x + 10$.

Step3: Substitute values from point (3,22)

When substituting the point $(x = 3,y = 22)$ into $y=4x + 10$, we get $22=4\times3 + 10$.
Left - hand side: $y = 22$.
Right - hand side: $4\times3+10=12 + 10=22$.

Answer:

The equation $y = 4x+10$ is correct as when $x = 3$, $y=4\times3 + 10=22$ which matches the table value. And for any pair $(x,y)$ in the table, they satisfy the equation $y = 4x + 10$.