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

What does the slope 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

Given the point (5, -1) and a slope of 2, write the equation in point-slope form.

Back

y + 1 = 2(x - 5) or y - (-1) = 2(x - 5).

Front

What is the slope of the line represented by the equation y - 3 = 2(x + 4)?

Back

The slope of the line is 2.

Front

How do you determine if a point lies on a line given in point-slope form?

Back

Substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.

Front

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

Back

The slope-intercept form is y = -1x + 5.

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

If a line has a slope of -3 and passes through the point (2, 4), what is the point-slope form of the equation?

Back

y - 4 = -3(x - 2).

Front

What is the relationship between the slope and the angle of inclination of a line?

Back

The slope of a line is equal to the tangent of the angle of inclination with respect to the positive x-axis.

Front

How can you identify the slope from the equation y + 5 = -3(x - 6)?

Back

The slope is the coefficient of (x), which is -3.