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 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

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

Back

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

Front

How do you find the y-intercept from the equation y = 2x + 5?

Back

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

Front

What is the first step to write the equation of a line given two points?

Back

Calculate the slope (m) using the two points.

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.

Front

What is the equation of the line that passes through (0, -2) and has a slope of -1?

Back

The equation is y = -x - 2.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

Rearrange the equation Ax + By = C to solve for y in terms of x.