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

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, represented as (0, b).

Front

How do 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

If the slope of a line is 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Front

How do you graph the equation y = 3x + 1?

Back

Start at the y-intercept (0, 1). From there, use the slope (3) to go up 3 units and right 1 unit to plot another point.

Front

What is the y-intercept of the equation y = -rac{1}{2}x + 4?

Back

The y-intercept is (0, 4).

Front

How can you convert the equation 2x - 3y = 6 into slope-intercept form?

Back

Rearranging gives y = rac{2}{3}x - 2, where the slope is rac{2}{3} and the y-intercept is -2.

Front

What is the slope of the line represented by the equation y = -4x + 5?

Back

The slope is -4.

Front

If a line has a slope of 0, what does this indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning y remains constant regardless of x.