Writing Equations of Lines

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you convert point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

How do you find the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

Write the equation of a line in slope-intercept form given slope m and y-intercept b.

Back

The equation of the line is y = mx + b.

Front

What is the relationship between parallel lines and their slopes?

Back

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

Front

What is the relationship between perpendicular lines and their slopes?

Back

Perpendicular lines have slopes that are negative reciprocals of each other (m1 * m2 = -1).

Front

Write the equation of a line with slope 3 and y-intercept -2.

Back

The equation is y = 3x - 2.

Front

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

Back

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