Writing Linear Equations

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope in the equation y = 4x + 6?

Back

In the equation y = 4x + 6, the slope (m) is 4.

Front

What does the y-intercept represent in the equation y = -2x + 3?

Back

In the equation y = -2x + 3, the y-intercept (b) is 3, which means the line crosses the y-axis at the point (0, 3).

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What is the slope of the line represented by the equation y = (2/5)x - 1?

Back

The slope of the line represented by the equation y = (2/5)x - 1 is 2/5.

Front

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

Back

The slope indicates the rate of change of y with respect to x; it shows how steep the line is and the direction it goes (positive or negative).

Front

How do you find the y-intercept from the equation y = 3x + 16?

Back

The y-intercept can be found by setting x = 0 in the equation. For y = 3x + 16, when x = 0, y = 16.

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 do you graph a linear equation using the slope and y-intercept?

Back

To graph a linear equation, start at the y-intercept on the y-axis, then use the slope (rise/run) to find another point on the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.