Point Slope Form to Slope-Intercept Form

Front

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

Back

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

Front

How do you write the equation of a line in point-slope form given a point and a slope?

Back

To write the equation in point-slope form, use the formula: y - y₁ = m(x - x₁), substituting (x₁, y₁) for the given point and m for the slope.

Front

Convert the point-slope equation y - 5 = -3(x - 10) to slope-intercept form.

Back

To convert to slope-intercept form, distribute and simplify: y = -3x + 30 + 5, which simplifies to y = -3x + 35.

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

Write the equation of the line that passes through the points (0, -5) and (4, 3) in slope-intercept form.

Back

First, find the slope: m = (3 - (-5)) / (4 - 0) = 2. Then use the point-slope form: y - (-5) = 2(x - 0), which simplifies to y = 2x - 5.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how much y changes for a unit change in x.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

If a line has an undefined slope, what does that indicate about the line?

Back

An undefined slope indicates a vertical line, meaning x remains constant while y changes.

Front

How do you transform the equation y - 2 = 3(x + 4) into slope-intercept form?

Back

Distribute and simplify: y - 2 = 3x + 12, then add 2 to both sides to get y = 3x + 14.