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 the formula: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

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

Back

In the point-slope form y - y_1 = m(x - x_1), the slope m is the coefficient of (x - x_1).

Front

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

Back

To convert, distribute and rearrange: y - 2 = 3x + 3 => y = 3x + 5.

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

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

Back

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

Front

What is the slope of the line given by the equation y + 1 = -3(x - 5)?

Back

The slope of the line is -3.

Front

How do you convert the equation y - 2 = 9(x + 1) into slope-intercept form?

Back

Distribute and rearrange: y - 2 = 9x + 9 => y = 9x + 11.

Front

What is the significance of the point (x_1, y_1) in the point-slope form?

Back

The point (x_1, y_1) is a specific point on the line that the equation represents.

Front

Identify the slope in the equation y + 1 = -rac{1}{2}(x - 1).

Back

The slope is -rac{1}{2}.

Front

What is the point-slope form equation for the point (3, 4) with a slope of 2?

Back

The point-slope form is y - 4 = 2(x - 3).