Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when it is 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 of a linear equation represent?

Back

The slope represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the unit rate from a given total and quantity?

Back

To find the unit rate, divide the total amount by the quantity. For example, if Elijah earns $200 for 8 hours of work, the unit rate is $200 ÷ 8 = $25 per hour.

Front

What is the initial value in a linear equation context?

Back

The initial value is the y-intercept of the linear equation, representing the starting point of the relationship when x is 0.

Front

How can you determine the equation of a line from a table of values?

Back

To determine the equation, identify the slope (change in y over change in x) and the y-intercept from the table, then use the slope-intercept form y = mx + b.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two variables to be directly proportional?

Back

Two variables are directly proportional if they increase or decrease at the same rate, which can be represented by a linear equation through the origin.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients indicate the relationship between the variables; the coefficient of x represents the slope, while the constant term represents the y-intercept.

Front

How do you graph a linear equation?

Back

To graph a linear equation, plot the y-intercept on the y-axis, use the slope to find another point, and draw a straight line through the points.