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 point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you identify the slope from a linear equation in the form y = mx + b?

Back

The slope is the coefficient of x (m) in the equation.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How can you determine if a table of values represents a linear relationship?

Back

If the differences between the y-values are constant for equal intervals of x, then the relationship is linear.

Front

What is the equation for a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.

Front

If Ryan builds 4 picnic tables each day and starts with 2 tables, what is the equation for the total number of tables after d days?

Back

t = 4d + 2.

Front

What does the equation y = -2x + 5 represent?

Back

This equation represents a linear relationship where the slope is -2 and the y-intercept is 5.

Front

How do you find the total cost of shipping a package based on its weight using the equation y = 1.50x + 6?

Back

In this equation, y is the total cost, x is the weight of the package, 1.50 is the cost per unit weight, and 6 is the base cost.