Equations of a Line Review

Front

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

Back

The slope-intercept form is 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 as 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 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 b in the slope-intercept form.

Front

Write the equation of a line with a slope of 3 that passes through the point (0, 2).

Back

y = 3x + 2.

Front

What is the equation of a line that passes through the points (1, 2) and (3, 6)?

Back

y = 2x.

Front

How do you convert the standard form of a line Ax + By = C to slope-intercept form?

Back

Solve for y to get y = (-A/B)x + (C/B).

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.

Front

What is the significance of an undefined slope?

Back

An undefined slope indicates a vertical line, meaning x is constant regardless of y.

Front

If a line has a slope of -1, what does this indicate about the line's direction?

Back

The line decreases from left to right, indicating a negative relationship between x and y.