Writing Equations of Lines

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

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

Front

What is a y-intercept?

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 -2 through the point (7, −1).

Back

y = -2x + 13.

Front

Write the equation of a line with slope 3/5 through the point (20, 6).

Back

y = 3/5x - 6.

Front

Write the equation of a line through the points (4, 5) and (12, 9).

Back

y = 1/2x + 3.

Front

Write the equation of a line with slope 5/2 through the point (8, −2).

Back

y = 5/2x - 22.

Front

What is the formula to convert a slope and a point into the equation of a line?

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 significance of a positive slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.