Writing Equations of Lines

Front

What is the 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 equation of a line given a slope and a point?

Back

To find the equation of a line given a slope (m) and a point (x₀, y₀), use the point-slope form: y - y₀ = m(x - x₀). You can then rearrange it to slope-intercept form.

Front

What does the slope of a line represent?

Back

The slope of a line 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 of a line is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

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

Back

To convert from point-slope form (y - y₀ = m(x - x₀)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How do you determine the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are the two points.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.