Standard Form to Slope Intercept Form FLASHCARD

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 2x + 4y = 8 into slope-intercept form?

Back

To convert, first subtract 2x from both sides: 4y = -2x + 8. Then divide by 4: y = -\frac{1}{2}x + 2.

Front

What is the first step to solve for y in the equation 2x + 4y = 8?

Back

Subtract 2x from each side.

Front

What is the slope of the equation 12x - 6y = 30?

Back

To find the slope, convert to slope-intercept form: -6y = -12x + 30, then y = 2x - 5. The slope is 2.

Front

How do you determine the slope and y-intercept from the equation 4x + y = -10?

Back

Rearrange to slope-intercept form: y = -4x - 10. The slope is -4 and the y-intercept is (0, -10).

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 y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form y = mx + b.

Front

How can you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope m can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the slope being positive, negative, or zero?

Back

A positive slope indicates the line rises, a negative slope indicates it falls, and a zero slope indicates a horizontal line.

Front

What is the graphical representation of the equation 5x + 2y = 10?

Back

To graph, convert to slope-intercept form: 2y = -5x + 10, then y = -\frac{5}{2}x + 5.