8-6.2 FLASHCARD 2023-2024 GRAPH 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 m is the slope and (x₁, y₁) is a point on the line.

Front

How do you identify the slope from the point-slope form equation?

Back

In the equation y - y₁ = m(x - x₁), the slope (m) is the coefficient of (x - x₁).

Front

Back

The slope of the equation is -1.

Front

Back

The line passes through the point (-4, 3).

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

How can you convert point-slope form to slope-intercept form?

Back

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

Front

What is the significance of the point (x₁, y₁) in point-slope form?

Back

The point (x₁, y₁) is a specific point on the line, which can be used to find the equation of the line.

Front

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

Back

A slope of 2 indicates that for every 1 unit increase in x, y increases by 2 units, making the line relatively steep.

Front

What is the point-slope form equation for a line with slope 3 passing through the point (-3, 4)?

Back

The point-slope form equation is: y - 4 = 3(x + 3).

Front

How do you determine if a point lies on a line represented by a point-slope equation?

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.