slope intercept to general form calculator

How to Convert Slope Intercept Form to General Form Calculator

When it comes to mathematics, understanding the different forms of linear equations is crucial. One such form is the slope-intercept form, which is represented as y = mx + b, where m is the slope and b is the y-intercept. However, sometimes you may need to convert this equation into its general form, Ax + By = C. This is where a slope intercept to general form calculator comes in handy.

To use this calculator, you will need two points that lie on the line. These points are typically represented as (x₁, y₁) and (x₂, y₂). First, construct the slope-intercept form using these values. For example, let's say you have the points (2, 3) and (4, 5).

To find the slope, use the slope-intercept formula: m = (y₂ - y₁) / (x₂ - x₁). In this case, m = (5 - 3) / (4 - 2) = 1. So, the slope is 1.

Next, substitute one of the points into the equation to find the y-intercept. Let's use the first point (2, 3). Substitute x = 2 and y = 3 into the equation: 3 = m(2) + b. Since we know the slope is 1, the equation becomes 3 = 1(2) + b. Solving for b, we get b = 1.

Now that you have the slope and y-intercept, you can write the slope-intercept form of the equation: y = mx + b. In this case, the equation is y = x + 1.

To convert this equation to its general form, Ax + By = C, follow these steps:

1. Subtract the first equation from the second to eliminate the y-term.

2. Divide both sides of the equation by (x₂ - x₁) to identify the slope.

3. Substitute the two points' coordinates into the equation.

For example, let's convert the equation y = x + 1 to its general form. First, subtract the first equation from the second: 0 = x + 1 - (2, 3). Simplify the equation to get 0 = x - 2.

Next, divide both sides of the equation by (4 - 2) = 2: 0 = (x - 2)/2.

Finally, substitute the two points' coordinates into the equation. For example, if we substitute x = 2 and y = 3, we get 3 = 1(2) + 1.

As you can see, converting slope intercept form to general form can be a bit involved. However, with a calculator like this, it's much easier to find the equation of a line in its general form. Whether you're working with linear equations or need to solve for x and y-intercepts, this calculator is an essential tool to have in your math toolkit.

Slope intercept to general form calculator