Equations from two points

Front

What is the formula to find 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

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 Slope-Intercept Form of a linear equation?

Back

The Slope-Intercept Form is given by: y = mx + b, where m is the slope and b is the y-intercept.

Front

If the slope of a line is -3 and it passes through the point (1, 2), what is the equation of the line in Slope-Intercept Form?

Back

Using the point-slope form: y - 2 = -3(x - 1) simplifies to y = -3x + 5.

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, represented by the value of b in the equation y = mx + b.

Front

How do you convert the standard form of a linear equation Ax + By = C to Slope-Intercept Form?

Back

Rearrange the equation to solve for y: y = (-A/B)x + (C/B).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

Given the points (1, 2) and (3, 6), find the equation of the line in Slope-Intercept Form.

Back

The slope is m = (6 - 2) / (3 - 1) = 2. The equation is y = 2x. (b = 0).

Front

If a line has a slope of 1 and passes through the origin, what is its equation?

Back

The equation is y = x.