Slope and Equation of a Line

Front

What is the slope of a line?

Back

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

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 of a line that passes through the points (0, 1) and (2, 6)?

Back

m = 5/2.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + c, where m is the slope and c is the y-intercept.

Front

What does 'c' represent in the equation y = mx + c?

Back

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

Front

How do you write the equation of a line given its slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

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

Back

The y-intercept is 3.

Front

Find the equation of the line that passes through the points (-2, 4) and (1, 10).

Back

y = 2x + 8.

Front

What is the slope of the line represented by the equation y = 1/3x - 2?

Back

The slope is 1/3.

Front

What is the x-intercept of the line y = -3x - 2?

Back

To find the x-intercept, set y = 0: 0 = -3x - 2, so x = -2/3.