Slope and Slope Intercept

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation, which is defined as the ratio of the rise (change in y) to the run (change in x).

Front

How do you calculate 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

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 y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of 'b' in the slope-intercept form.

Front

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

Write the equation of a line with a slope of 2 that passes through the point (1, 3).

Back

Using the point-slope form, the equation is y - 3 = 2(x - 1), which simplifies to y = 2x + 1.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line descends steeply from left to right.

Front

Find the slope of the line passing through the points (2, 4) and (6, 12).

Back

The slope is m = (12 - 4) / (6 - 2) = 8 / 4 = 2.