Writing Equations in Standard and Point Slope Forms

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 (m) between two points (x₁, y₁) and (x₂, y₂)?

Back

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

Front

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

Back

y = 3x - 1.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1 (m₁ * m₂ = -1).

Front

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

Back

y - 3 = 4(x - 2).

Front

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

Back

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

Front

Convert the equation y = 2x + 5 into point-slope form using the point (1, 7).

Back

y - 7 = 2(x - 1).

Front

If the equation of a line is y = -x + 4, what is the slope?

Back

The slope (m) is -1.

Front

What is the y-intercept of the equation y = 3x - 2?

Back

The y-intercept is -2.