Standard Form to Slope-Intercept Form

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 convert an equation from standard form to slope-intercept form?

Back

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

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, indicating how steep the line is and the direction it goes (positive or negative).

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) represents the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

Given the equation 5x - 3y = -9, what is the first step to convert it to slope-intercept form?

Back

The first step is to isolate y by moving the term with x to the other side of the equation.

Front

What is the slope of the line represented by the equation 3x - 6y = 12?

Back

To find the slope, convert the equation to slope-intercept form; the slope is 1/2.

Front

In the equation y = (5/3)x + 3, what is the slope and y-intercept?

Back

The slope is 5/3 and the y-intercept is 3.

Front

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

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

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

Back

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

Front

How can you identify the slope from the equation -3y + 5x = 12?

Back

Rearrange the equation to slope-intercept form to identify the slope, which is 5/3.