Linear Equations in All Forms

Front

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

Back

The point-slope form is given by the equation 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 form equation y - y1 = m(x - x1) to get y = mx + b.

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

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 standard form of a linear equation?

Back

The standard form is given by the equation ax + by = c, where a, b, and c are integers and a ≥ 0.

Front

How do you find the y-intercept from the slope-intercept form?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

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

Back

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

Front

What is the relationship between parallel lines in terms of slope?

Back

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

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other.