Standard Form

Front

What is the slope-intercept form of a line?

Back

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

Front

How do you find the slope from the equation of a line in standard form?

Back

To find the slope from the standard form Ax + By = C, rearrange the equation to slope-intercept form (y = mx + b) and identify m.

Front

What are x- and y-intercepts?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is where the line crosses the y-axis (x=0).

Front

How do you calculate the x-intercept of the equation 5x - 3y = 15?

Back

Set y = 0 in the equation: 5x - 3(0) = 15, which simplifies to x = 3. So, the x-intercept is (3, 0).

Front

How do you calculate the y-intercept of the equation 5x - 3y = 15?

Back

Set x = 0 in the equation: 5(0) - 3y = 15, which simplifies to y = -5. So, the y-intercept is (0, -5).

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the meaning of a positive slope?

Back

A positive slope indicates that as x increases, y also increases, showing an upward trend.

Front

What is the meaning of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing a downward trend.

Front

How do you convert the equation 7x + 2y = -28 to slope-intercept form?

Back

Rearranging gives y = -rac{7}{2}x - 14.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x = 0; it indicates where the line crosses the y-axis.