Writing equations from two points

Front

What is the slope of a line that passes through the points (2, 9) and (3, 1)?

Back

The slope (m) is calculated as (y2 - y1) / (x2 - x1) = (1 - 9) / (3 - 2) = -8.

Front

What is the slope-intercept form of a line?

Back

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

Front

How do you find the y-intercept of a line given its slope and a point?

Back

Use the slope-intercept form y = mx + b. Substitute the slope (m) and the coordinates of the point (x, y) to solve for b.

Front

What is the equation of the line that has a slope of 3 and passes through the point (-1, 9)?

Back

The equation is y = 3x + 12.

Front

How do you write the equation of a line given two points?

Back

First, calculate the slope (m) using the formula (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What is the point-slope form of a line?

Back

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

Front

What is the equation of the line that passes through the points (0, 3) and (-4, -1)?

Back

The equation is y = x + 3.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What is the equation of the line that passes through the points (3, 3) and (4, -1)?

Back

The equation is y = -4x + 15.

Front

What does it mean for a line to have a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.