Writing Equations (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 convert a point and slope into point-slope form?

Back

To convert a point (x₁, y₁) and slope m into point-slope form, use the formula: y - y₁ = m(x - x₁).

Front

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

Back

y - 2 = 4(x - 3).

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

If a line has a slope of -2, what does this indicate about the line's direction?

Back

A slope of -2 indicates that the line descends from left to right, meaning for every 1 unit increase in x, y decreases by 2 units.

Front

Write the equation in point-slope form for the point (1, -1) with a slope of 3.

Back

y + 1 = 3(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 that the equation represents.

Front

Convert the equation y - 4 = 2(x + 1) into slope-intercept form.

Back

y = 2x + 6.

Front

What is the slope of the line represented by the equation y - 5 = -1(x - 2)?

Back

The slope is -1.

Front

Write the equation in point-slope form for the point (0, 0) with a slope of 5.

Back

y = 5x.