Writing 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) between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as 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 the points (0, 3) and (-4, -1), what is the slope of the line?

Back

The slope m is ( -1 - 3 ) / ( -4 - 0 ) = 4/4 = 1.

Front

What is the equation of a line with a slope of -2 that passes through the point (1, 4)?

Back

Using the point-slope form: y - 4 = -2(x - 1) simplifies to y = -2x + 6.

Front

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

Back

Start with y - y1 = m(x - x1) and solve for y to get y = mx + (y1 + m(-x1)).

Front

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

Back

The slope indicates the steepness and direction of the line; a positive slope rises, while a negative slope falls.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line.

Front

What is the equation of a line that passes through the points (2, 3) and (4, 7)?

Back

First, find the slope: m = (7 - 3) / (4 - 2) = 2. Then use point-slope form: y - 3 = 2(x - 2) simplifies to y = 2x - 1.

Front

How do you find the y-intercept from the equation y = 3x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.