Ask AI: How do convert two points to a slope intercept?

To convert two points into the slope-intercept form of a linear equation, which is \(y = mx + b\), you need to find the slope \(m\) and the y-intercept \(b\). Suppose you're given two points: \((x_1, y_1)\) and \((x_2, y_2)\). Here are the steps to follow: 1. **Calculate the slope (\(m\)):** The formula to find the slope between two points is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] 2. **Use the slope to find the y-intercept (\(b\)):** You can use the slope and one of the given points to find \(b\). Let's use the point \((x_1, y_1)\). Plug these values into the slope-intercept equation: \[ y_1 = mx_1 + b \] Solve for \(b\): \[ b = y_1 - mx_1 \] 3. **Write the equation in slope-intercept form:** Now that you have both \(m\) and \(b\), you can write the equation as: \[ y = mx + b \] **Example:** Let's say you have the points \((2, 3)\) and \((4, 7)\). 1. Calculate the slope: \[ m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \] 2. Find the y-intercept using point \((2, 3)\): \[ 3 = 2(2) + b \] \[ 3 = 4 + b \] \[ b = 3 - 4 = -1 \] 3. Write the equation: \[ y = 2x - 1 \] This is the equation of the line in slope-intercept form that passes through the points \((2, 3)\) and \((4, 7)\).

To convert two points to a slope intercept, first determine the slope of the line by using the equation m = (y₂-y₁)/(x₂-x₁). Then, use one of the points to calculate the y-intercept, b = y₁ - mx₁. Finally, the slope intercept equation is y = mx + b.