Slope & Writing Equations of Lines

Front

What is the slope of a line?

Back

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

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

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

How do you write the equation of a line given a 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 relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one slope is m, the other is -1/m.

Front

How do you convert the standard form of a line to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/B).

Front

What is the equation of a line with a slope of -2 that passes through the point (7, -1)?

Back

The equation is y = -2x + 13.

Front

What is the equation of a line with a slope of 25 and a y-intercept of 500?

Back

The equation is y = 25x + 500.