Point-Slope Equations

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 write an equation in point-slope form given a point and a slope?

Back

To write an equation in point-slope form, use the formula y - y1 = m(x - x1), substituting (x1, y1) with the given point and m with the given slope.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is and the direction it goes (positive or negative).

Front

Given the point (2, 3) and a slope of 5, write the equation in point-slope form.

Back

y - 3 = 5(x - 2).

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, and it is used to anchor the equation to that location on the graph.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

How can you convert a point-slope equation to slope-intercept form?

Back

To convert to slope-intercept form (y = mx + b), solve for y in the point-slope equation y - y1 = m(x - x1).

Front

What is the slope of the line represented by the equation y = -2/3(x + 4) + 1?

Back

The slope of the line is -2/3.

Front

Determine a point on the line given by the equation y = 1/2(x - 6) + 3.

Back

One point on the line is (6, 3).

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.