Writing Equations of Lines

Front

What is the slope-intercept form of a line?

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

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

Back

y = 1x + 1.

Front

Write the equation of a line with slope -3 through the point (4, 2).

Back

y = -3x + 14.

Front

What is the point-slope form of a line?

Back

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

Front

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

Back

To convert, solve for y in the point-slope equation y - y1 = m(x - x1) to get y = mx + b.

Front

Write the equation of a line with slope 2 through the point (-1, 4).

Back

y = 2x + 6.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.