WU: Writing equations from two points

Front

What is the general form of a linear equation?

Back

The general form of a linear equation 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 using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept (b) represent in a linear equation?

Back

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

Front

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

Back

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

Front

What is the equation of a line with a slope of 2 that passes through the point (1, 3)?

Back

Using the point-slope form, the equation is y - 3 = 2(x - 1), which simplifies to y = 2x + 1.

Front

How do you convert the equation 3x - 4y = 12 into slope-intercept form?

Back

To convert to slope-intercept form, solve for y: 4y = 3x - 12, so y = (3/4)x - 3.

Front

What is the significance of the line of best fit in data analysis?

Back

The line of best fit represents the trend in the data, minimizing the distance between the data points and the line.

Front

How can 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 formula for finding the equation of a line given two points?

Back

First, calculate the slope (m) using the two points, then use the point-slope form to write the equation.

Front

If a line has a slope of -1, what does this indicate about its direction?

Back

A slope of -1 indicates that the line decreases at a 45-degree angle from left to right.