Point-Slope Form Flashcard

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by the equation: 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 equation y - y_1 = m(x - x_1), the slope m is the coefficient of (x - x_1).

Front

What does the point (6, -5) represent in the equation y + 5 = -3(x - 6)?

Back

It is a point that lies on the line represented by the equation.

Front

Convert the point-slope form y + 1 = 2(x - 5) to slope-intercept form.

Back

The slope-intercept form is y = 2x - 9.

Front

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

Back

The slope is 2.

Front

If a line has a slope of 3, what does this indicate about the line's steepness?

Back

A slope of 3 indicates that for every 1 unit increase in x, y increases by 3 units, making the line steep.

Front

What is the significance of the point (5, -1) in the context of point-slope form?

Back

It is a specific point through which the line passes.

Front

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

Back

Substitute the x and y coordinates of the point into the equation. If the equation holds true, the point lies on the line.

Front

What is the slope of the line represented by the equation y + 9 = 3(x - 1)?

Back

The slope is 3.

Front

What does the term 'slope' refer to in a linear equation?

Back

The slope refers to the rate of change of y with respect to x, indicating how steep the line is.