Slope & Slope-Intercept

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is calculated as the ratio of the rise (change in y) over the run (change in x).

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 find the y-intercept of a line given a point and slope?

Back

To find the y-intercept (b), use the formula: b = y - mx, where (x, y) is the given point and m is the slope.

Front

What does the y-intercept represent in a graph?

Back

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

Front

If a line has a slope of 0, what does that indicate?

Back

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

Front

If a line has an undefined slope, what does that indicate?

Back

An undefined slope indicates a vertical line, meaning there is no change in x as y changes.

Front

What is the slope of the line represented by the equation y = 5x + 2?

Back

The slope of the line is 5.

Front

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

Back

The y-intercept of the line is 4.

Front

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

Back

To convert, solve for y: 3y = -2x + 6, then y = -\frac{2}{3}x + 2.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2.