Writing Equations from Two Points

Front

What is the formula for finding the slope (m) between two points (x1, y1) and (x2, y2)?

Back

m = (y2 - y1) / (x2 - x1)

Front

How do you write the equation of a line in slope-intercept form?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

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

Back

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

y - 2 = 3(x - 1) or y = 3x - 1.

Front

What is the point-slope form of a linear equation?

Back

y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Front

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

Back

Isolate y to get y = mx + b.

Front

What is the significance of a slope of 0 in a linear equation?

Back

A slope of 0 indicates a horizontal line.

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that the line is decreasing from left to right.

Front

How do you find the y-intercept from two points?

Back

First, find the slope, then use one point to solve for b in y = mx + b.