Slope and y=mx+b

Front

What is the slope of a line?

Back

The slope of a line (m) is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 'b' represent in the equation y = mx + b?

Back

The 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

Front

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

Back

A slope of 0 indicates that the line is horizontal.

Front

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

Back

An undefined slope indicates that the line is vertical.

Front

How do you find the y-intercept from the equation of a line?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Back

The slope (m) is calculated as m = (7 - 3) / (4 - 2) = 2.

Front

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

Back

Using the point-slope form: y - 2 = 3(x - 1) simplifies to y = 3x - 1.

Front

What is the slope of the line that passes through the points (0, 5) and (10, 15)?

Back

The slope (m) is calculated as m = (15 - 5) / (10 - 0) = 1.