Slope-Intercept Form Calculator

About Slope-Intercept Form Calculator

Slope-intercept form: y = mx + b where m is slope and b is y-intercept. Standard form: Ax + By = C.

How to use this calculator

1. Enter the two points into the calculator.
2. Use the points to find the slope.
3. Use one point and the slope to solve for the y-intercept.
4. Write the final equation in slope-intercept form.

The formula explained

• \(m\) = slope
• \(b\) = y-intercept
• \(x_1, y_1\) = the first point
• \(x_2, y_2\) = the second point
• \(x, y\) = coordinates on the line

Step by step method

1. Start with two points, such as \((1, 3)\) and \((5, 11)\).
2. Find the slope by subtracting the y-values and dividing by the difference in x-values.
3. Substitute the slope and one point into \(y = mx + b\) to find \(b\).
4. Write the equation as \(y = mx + b\).

Worked example

Suppose you want the line that passes through the points (2, 5) and (6, 13).

1. Find the slope: \(m = \frac{13 - 5}{6 - 2} = \frac{8}{4} = 2\).
2. Use one point, such as \((2, 5)\), in \(y = mx + b\): \(5 = 2(2) + b\).
3. Solve for \(b\): \(5 = 4 + b\), so \(b = 1\).
4. Write the equation: \(y = 2x + 1\).

Tips and common mistakes

• Make sure the two points are not the same point, or the slope cannot be found.
• Keep the x-values paired with the correct y-values from each point.
• Watch the signs carefully when subtracting coordinates.
• If the line is vertical, slope-intercept form does not apply.

Frequently asked questions