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 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

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

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line is decreasing; for every 1 unit increase in x, y decreases by 3 units.

Front

Write the point-slope form for a line with slope 2 that passes through the point (1, 4).

Back

y - 4 = 2(x - 1).

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 anchor the equation.

Front

How can you convert 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 given by the equation y - 2 = 3(x + 1)?

Back

The y-intercept is 5, found by rewriting the equation in slope-intercept form.

Front

Identify the slope and y-intercept from the equation y = -2x + 3.

Back

The slope is -2 and the y-intercept is 3.

Front

What is the equation of a line in point-slope form that passes through (0, 0) with a slope of 4?

Back

y = 4x.