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

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

What does the point (x1, y1) represent in the point-slope form?

Back

The point (x1, y1) represents a specific point on the line described by the equation.

Front

If a line has a slope of -3, what does this indicate about its direction?

Back

A slope of -3 indicates that for every 1 unit increase in x, the value of y decreases by 3 units, meaning the line descends from left to right.

Front

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

Back

The slope-intercept form is y = 5x + 7.

Front

What is the slope of the line represented by the equation y + 1 = -2(x - 3)?

Back

The slope of the line is -2.

Front

Given the point (2, 3) and slope 4, write the equation in point-slope form.

Back

The equation is y - 3 = 4(x - 2).

Front

For the equation y - 4 = 3(x - 1), what point does the line pass through?

Back

The line passes through the point (1, 4).

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

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

Back

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