4.5 Standard 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 a standard form equation to slope-intercept form?

Back

To convert a standard form equation (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 of a line represent?

Back

The slope of a line 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 is the y-intercept in the slope-intercept form?

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 y = mx + b.

Front

How can you identify the slope from the equation y = 3x - 2?

Back

In the equation y = 3x - 2, the slope is 3, which is the coefficient of x.

Front

What is the first step to solve for slope-intercept form from the equation -x + 4y = 11?

Back

The first step is to add x to both sides of the equation to isolate the term with y.

Front

How do you find the slope from the equation 12x - 6y = 30?

Back

To find the slope, convert the equation to slope-intercept form (y = mx + b) and identify the coefficient of x.

Front

What is the slope of the line represented by the equation y = 4 - 6x?

Back

The slope of the line y = 4 - 6x is -6, which is the coefficient of x.

Front

What is the significance of the slope being negative?

Back

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

Front

What does it mean if the slope is zero?

Back

If the slope is zero, it means the line is horizontal, indicating that y does not change as x changes.