WSMS: 7th Accel. 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 y with respect to x. It indicates how much y changes for a unit change in x.

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 determine if a relationship is proportional?

Back

A relationship is proportional if it can be represented by a linear equation that passes through the origin (0,0). This means the ratio of y to x is constant.

Front

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

Back

The equation is y = 2x + 3.

Front

What does the fixed fee in a cost equation represent?

Back

The fixed fee represents the initial cost that does not change regardless of the number of units (e.g., miles) consumed.

Front

If a taxi charges $2.75 per mile, what does this value represent in the equation f(x) = 2.75x + 4.25?

Back

This value represents the slope of the equation, indicating the charge per mile.

Front

What is the general form of a linear equation?

Back

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

Front

How can you find the equation of a line given two points?

Back

To find the equation of a line given two points, calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), then use one of the points to solve for the y-intercept (b).

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as x increases, y decreases. The line falls from left to right.