Writing Equations of Lines

Front

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

Back

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

Front

How do you identify the slope from the slope-intercept form of an equation?

Back

In the slope-intercept form y = mx + b, the slope is represented by the coefficient m.

Front

What does the y-intercept represent in the slope-intercept form of a linear equation?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

How can you find the equation of a line given a slope and a point on the line?

Back

You can use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Front

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

Back

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

Front

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

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of a positive slope in a linear equation?

Back

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

Front

What does a negative slope indicate about a linear relationship?

Back

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

Front

How do you determine the slope from a graph of a line?

Back

The slope can be determined by selecting two points on the line and using the formula (y2 - y1) / (x2 - x1).

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0, indicating no change in y as x changes.