Converting forms of linear equations

Front

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

Back

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

Front

How do 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.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

Convert the equation 2x + 3y = 6 to slope-intercept form.

Back

y = -2/3x + 2.

Front

Convert the equation 4x - y = 8 to slope-intercept form.

Back

y = 4x - 8.

Front

What is the significance of the slope in the equation y = -6/5x - 3?

Back

The slope is -6/5, indicating that for every 5 units the x-value increases, the y-value decreases by 6 units.

Front

Convert the equation 5y = 15 - 10x to slope-intercept form.

Back

y = -2x + 3.

Front

How do you identify the slope from the equation y = 3/4x - 6?

Back

The slope is the coefficient of x, which is 3/4.

Front

What is the slope of the line represented by the equation y = -4/3x + 3?

Back

The slope is -4/3.