Slope Intercept and Point Slope Review

Front

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

Back

The point-slope form is given by the equation: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

Front

How do you find the slope between two points (x₁, y₁) and (x₂, y₂)?

Back

The slope (m) is calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁).

Front

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

Back

The slope-intercept form is given by the equation: 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, represented by the value of b in the slope-intercept form.

Front

How do you determine the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

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

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

Convert the equation 5x - 3y = 15 to slope-intercept form.

Back

Rearranging gives y = (5/3)x - 5.

Front

What are the x- and y-intercepts of the equation 2x + 3y = 6?

Back

The x-intercept is (3, 0) and the y-intercept is (0, 2).

Front

If a line has a slope of -2, what does this indicate about the line's direction?

Back

A slope of -2 indicates that for every 1 unit increase in x, y decreases by 2 units, meaning the line falls from left to right.

Front

What is the formula to convert from point-slope form to slope-intercept form?

Back

To convert, expand the point-slope form: y - y₁ = m(x - x₁) to get y = mx + (y₁ - mx₁).