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 y-intercept (b) represent in the equation y = mx + b?

Back

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

Front

Given points (2, 3) and (4, 7), what is the slope of the line?

Back

The slope m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If the slope of a line is -3 and it passes through the point (1, 2), what is the equation of the line?

Back

Using the point-slope form: y - 2 = -3(x - 1) simplifies to y = -3x + 5.

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, showing an upward trend.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning y remains constant regardless of x.

Front

How do you convert the equation 2x + 3y = 6 into slope-intercept form?

Back

Rearranging gives y = -2/3x + 2.

Front

What is the slope of the line represented by the equation y = 5x - 4?

Back

The slope is 5.

Front

If a line has a slope of 1/2, what does this mean in terms of rise over run?

Back

For every 2 units you move right (run), you move up 1 unit (rise).