October 2, 2025

What Is Point Slope Form

Q: How is point-slope form different from slope-intercept form?

Point-slope form (y - y₁ = m(x - x₁)) uses any point on the line. Slope-intercept form (y = mx + b) specifically uses the y-intercept (the point where x=0).

Q: Can you convert point-slope form to slope-intercept form?

Yes. Using the example y - 7 = 4(x - 2), first distribute the 4 to get y - 7 = 4x - 8. Then, add 7 to both sides to isolate y, resulting in y = 4x - 1.

Q: What information do you need to use the point-slope form?

You need exactly two pieces of information: the slope of the line (m) and the coordinates of one point (x₁, y₁) that the line passes through.

Q: If you have two points, can you still use this form?

Yes. If you have two points, you first use them to calculate the slope 'm'. Then you can pick either of the two points to be (x₁, y₁) and plug the values into the formula.

Learn what point-slope form is, its formula y - y₁ = m(x - x₁), and how to use it to write the equation of a line with a given point and slope.

Have More Questions →

What is Point-Slope Form?

Point-slope form is a way to write the equation of a straight line using its slope and the coordinates of any single point on the line. The general formula is y - y₁ = m(x - x₁), where 'm' represents the slope and (x₁, y₁) is the specific point.

Section 2: Key Components of the Formula

The formula contains three key values: 'm' is the slope, which measures the line's steepness. The coordinates (x₁, y₁) represent the known point on the line. The variables 'x' and 'y' represent the coordinates of any other point on the same line, defining the relationship between them.

Section 3: A Practical Example

Imagine a line has a slope of 4 and passes through the point (2, 7). In this case, m = 4, x₁ = 2, and y₁ = 7. Plugging these values into the point-slope formula gives you the equation: y - 7 = 4(x - 2).

Section 4: Why is Point-Slope Form Important?

Point-slope form is extremely useful when you know the slope of a line and a point it passes through, but not necessarily the y-intercept. It provides a direct and quick method to write the line's equation, which can then be easily converted into other forms like slope-intercept form.

Frequently Asked Questions

How is point-slope form different from slope-intercept form?

Can you convert point-slope form to slope-intercept form?

What information do you need to use the point-slope form?

If you have two points, can you still use this form?