Writing Equations of Lines (Point-Slope 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 calculate 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 of the line that passes through the points (10, 1) and (5, 2)?

Back

The slope is -1/5.

Front

Write the equation in point-slope form of the line that passes through (4, -7) with a slope of -1/4.

Back

y + 7 = -1/4(x - 4).

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

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

Back

A slope of 0 indicates that the line is horizontal.

Front

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

Back

An undefined slope indicates that the line is vertical.

Front

What is the significance of the point (x₁, y₁) in the point-slope form?

Back

The point (x₁, y₁) is a specific point on the line used to write the equation.

Front

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

Back

To convert, solve for y: y = mx + b, where b is the y-intercept.

Front

What is the y-intercept of the line represented by the equation y = 2x + 3?

Back

The y-intercept is 3.