Writing Linear Equations From Two Points

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 calculate the slope (m) from two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated using the formula 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 (b) in the slope-intercept form?

Back

The y-intercept is the value of y when x = 0; it is the point where the line crosses the y-axis.

Front

Given points (2, 3) and (4, 7), write the linear equation in slope-intercept form.

Back

y = 2x - 1.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

How do you find the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from Ax + By = C, set x = 0 and solve for y.

Front

What is the formula to convert a linear equation from standard form to slope-intercept form?

Back

Rearrange the equation Ax + By = C to solve for y: By = -Ax + C, then divide by B.

Front

Given the points (1, 2) and (3, 4), what is the slope?

Back

The slope m = (4 - 2) / (3 - 1) = 1.