Point slope Form

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 (x₁, y₁) is a point on the line and m is the slope.

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

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

Convert the point-slope form y - 2 = 3(x - 1) to slope-intercept form.

Back

The slope-intercept form is y = 3x - 1.

Front

Write the equation of a line in point-slope form that passes through (3, 2) with a slope of 4.

Back

y - 2 = 4(x - 3).

Front

What is the slope of the line represented by the equation y = 2x + 5?

Back

The slope is 2.

Front

If a line has a slope of -1, what does this indicate about the line's direction?

Back

A slope of -1 indicates that the line descends from left to right.

Front

Write the equation of a line in point-slope form that passes through (-1, -2) with a slope of -3.

Back

y + 2 = -3(x + 1).

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope.

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other.