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 between two points (x1, y1) and (x2, y2)?

Back

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

Front

If a line has a slope of 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

What is the y-intercept of the line represented by the equation y = 3x + 4?

Back

The y-intercept is 4, which means the line crosses the y-axis at the point (0, 4).

Front

How can you convert the equation y = -2x + 5 into slope-intercept form?

Back

The equation is already in slope-intercept form, where the slope is -2 and the y-intercept is 5.

Front

What is the equation of a line with a slope of 1 that passes through the point (0, 3)?

Back

The equation is y = 1x + 3 or simply y = x + 3.

Front

How do you determine the equation of a line given two points (x1, y1) and (x2, y2)?

Back

First, calculate the slope using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, meaning there is no change in y as x changes.