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 slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

Given the points (1, 2) and (3, 6), what is the slope of the line?

Back

The slope m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

Write the equation of a line with slope 2 that passes through the point (0, 1).

Back

The equation is y = 2x + 1.

Front

How do you convert the equation from standard form Ax + By = C to slope-intercept form?

Back

Solve for y to get y = (-A/B)x + (C/B).

Front

What is the equation of the 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) leads to y = 2x - 1.

Front

If a line has a slope of -1 and passes through (2, 4), what is its equation?

Back

The equation is y - 4 = -1(x - 2), which simplifies to y = -x + 6.

Front

What is the significance of the slope being zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.