Point Slope Form of a Line

Front

What is the point-slope form of a line?

Back

The point-slope form of a line 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

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

Given the points (3, -5) and (5, -1), what is the slope of the line connecting them?

Back

The slope is m = (-1 - (-5)) / (5 - 3) = 2.

Front

Convert the points (3, -5) and (5, -1) into point-slope form.

Back

The point-slope form is y + 5 = 2(x - 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

If a line has a slope of 2, what does this imply about the relationship between x and y?

Back

For every 1 unit increase in x, y increases by 2 units.

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 used to define the line's position.

Front

How can you identify the slope from the equation y - 4 = -1(x + 2)?

Back

The slope is the coefficient of (x), which is -1.

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

For the equation y - 3 = 2(x + 4), what is the slope and a point on the line?

Back

The slope is 2, and the point is (-4, 3).