Standard Form to Slope Intercept Form

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 equation 8x + 4y = 16 to slope-intercept form?

Back

First, isolate y: 4y = -8x + 16, then divide by 4: y = -2x + 4.

Front

What does the slope (m) represent in the slope-intercept form?

Back

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

Front

What does the y-intercept (b) represent in the slope-intercept form?

Back

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

Front

How do you solve for y in the equation -6x + 3y = 9?

Back

Add 6x to both sides: 3y = 6x + 9, then divide by 3: y = 2x + 3.

Front

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

Back

Add x to both sides to isolate the term with y.

Front

Convert the equation 3x + y = 12 to slope-intercept form.

Back

Isolate y: y = -3x + 12.

Front

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

Back

Isolate y: y = -5x - 10.

Front

What is the significance of the slope in a real-world context?

Back

The slope can represent speed, growth rate, or any other rate of change in real-world applications.

Front

If the slope of a line is negative, what does that indicate about the line's direction?

Back

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