Find linear equations given a point & a slope or two points

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 equation of a line given a point and a slope?

Back

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

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

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal and does not rise or fall as x changes.

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

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

Back

Rearrange the equation y - y1 = m(x - x1) to isolate y, resulting in y = mx + (y1 - mx1).

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the formula to find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

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

Back

y = 2x - 2.