Point-Slope Form Practice

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 m is the slope and (x₁, y₁) is a point on the line.

Front

How do you convert the equation y - 2 = -4x + 16 into slope-intercept form (y = mx + b)?

Back

To convert to slope-intercept form, add 2 to both sides to get y = -4x + 18.

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 the slope of a line is -4, what does this indicate about the line's direction?

Back

A slope of -4 indicates that the line descends steeply from left to right.

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 helps define the line's position.

Front

How can you find a point on a line given its equation in point-slope form?

Back

You can substitute any value for x into the equation to find the corresponding y value, thus finding a point on the line.

Front

What is the slope of the line given by the equation y + 2 = 6(x + 7)?

Back

The slope (m) of the line is 6.

Front

What is the first step to convert the equation y + 3 = -4(x - 9) into slope-intercept form?

Back

The first step is to distribute -4 to (x - 9) and then isolate y.

Front

Write the equation of a line in point-slope form that passes through the point (10, 5) with a slope of -3.

Back

The equation is y - 5 = -3(x - 10).

Front

What does it mean if two lines have the same slope?

Back

If two lines have the same slope, they are parallel and will never intersect.