Use the Point-Slope Form Graph Calculator to easily graph a line given a point and a slope.

Understanding Point-Slope Form

The point-slope form of a linear equation is a way to express the equation of a line when you know a point on the line and the slope. The formula is given by:

y - y₁ = m(x - x₁)

Where:

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

This form is particularly useful because it allows you to quickly write the equation of a line when you have a specific point and the slope. For example, if you have a slope of 2 and a point (3, 4), the equation would be:

y - 4 = 2(x - 3)

How to Use the Point-Slope Form Graph Calculator

To use the Point-Slope Form Graph Calculator, follow these steps:

  1. Input the x-coordinate of the point on the line.
  2. Input the y-coordinate of the point on the line.
  3. Input the slope of the line.
  4. Click the “Graph Line” button to see the equation and graph.

This calculator simplifies the process of graphing lines and helps visualize the relationship between the slope and the points on the line.

Example Problem

Consider a line with a slope of 3 that passes through the point (2, 5). Using the point-slope form, the equation can be expressed as:

y - 5 = 3(x - 2)

This equation can be rearranged to slope-intercept form (y = mx + b) if needed, but the point-slope form is often more convenient for graphing.

FAQ

1. What is the point-slope form used for?

The point-slope form is used to write the equation of a line when you know a point on the line and the slope.

2. How do I convert point-slope form to slope-intercept form?

You can rearrange the equation by solving for y to convert it to slope-intercept form (y = mx + b).

3. Can I use this calculator for any slope?

Yes, you can input any slope value, including negative slopes, to graph the corresponding line.

4. What if I don’t know the slope?

If you don’t know the slope, you can calculate it using two points on the line with the formula: m = (y₂ – y₁) / (x₂ – x₁).

5. Is the calculator accurate?

The calculator provides an accurate representation of the line based on the inputs provided. For precise graphing, ensure your inputs are correct.