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Linear Equations Basics

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Linear Equations Basics

Choose the best answer where options are provided. Show your calculations for solving questions.

Understanding Linear Equations

1.Which description best fits a linear equation in two variables?

An equation whose graph is a straight line
An equation that contains only addition
An equation with no variables

2.In the equation y = 4x + 7, which number is the coefficient of x?

3.Which choice lists both variables in the equation 6a + b = 19?

6 and 19
a and b
6 and b
a and 19

4.A dog-walking service pays $9 for each hour worked. Let h be hours and p be pay in dollars. Which equation represents the pay?

p = h + 9
p = 9h
p = 9 + h

Evaluating and Using Equations

5.Evaluate y = 4x when x = 5. Find y.

6.Use y = x + 6 to complete the outputs for the given inputs: x = 2, x = 4, and x = 7.

x (input)

y (output)

_____

7.For y = 2x - 3, calculate y when x = 6. Include the substitution you used.

8.For y = 5x, describe how y changes whenever x increases by 1.

Linear Equations in Context

9.A bike rental costs a $6 starting fee plus $3 per hour. Write an equation for total cost c in dollars after h hours.

10.Use the equation you wrote for the bike rental to find the cost for 4 hours. Show your calculation.

11.A school club sells notebooks for $2 each and starts with $5 in its cash box. Let n be the number of notebooks sold and m be the total amount of money in dollars. Write an equation for m, then find m when n = 3.