Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division).

Front

What is the solution to the equation 7x + 19 = -2x + 55?

Back

The solution is x = 4.

Front

What is the solution to the equation 3(x - 2) = 18?

Back

The solution is x = 8.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express it in the form y = mx + b.

Front

What is the cost equation for renting movies if the rental card costs $10 and each movie costs $2?

Back

The cost equation is y = 2x + 10, where y is the total cost and x is the number of movies rented.

Front

What is the equation for the total cost of downloading songs if the startup cost is $7.95 and each song costs $0.95?

Back

The equation is y = 0.95x + 7.95, where y is the total cost and x is the number of songs downloaded.

Front

How do you represent a situation with two variables in a linear equation?

Back

You can represent it using the form ax + by = c, where a and b are coefficients, x and y are variables, and c is a constant.