Writing Equations of Lines Given a Graph

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 a line?

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?

Back

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

Front

How can you determine the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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 convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to isolate it on one side: y = (-A/B)x + (C/B).

Front

What is the slope of a horizontal line?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero when calculating the slope.

Front

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

Back

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