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

Back

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

Front

Given the points (3, -5) and (5, -1), what is the slope of the line connecting them?

Back

The slope m is calculated as m = (-1 - (-5)) / (5 - 3) = 2.

Front

How do you convert a point-slope equation to slope-intercept form?

Back

To convert from point-slope form (y - y₁ = m(x - x₁)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the slope-intercept form of the equation y + 5 = -3(x - 6)?

Back

The slope-intercept form is y = -3x + 13.

Front

What does the variable 'm' represent in the point-slope form of a linear equation?

Back

In the point-slope form, 'm' represents the slope of the line.

Front

If a line has a slope of -1/4 and passes through the point (4, -7), what is its equation in point-slope form?

Back

The equation in point-slope form is y + 7 = -1/4(x - 4).

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 define the line's equation in point-slope form.

Front

How can you identify the slope from the equation y = mx + b?

Back

In the equation y = mx + b, 'm' is the coefficient of x and represents the slope of the line.

Front

What is the first step to convert y + 5 = -3(x - 6) into slope-intercept form?

Back

The first step is to distribute -3 to both terms in the parentheses: y + 5 = -3x + 18.