How do you write an equation in slope-intercept form when given a slope and a point?

To write an equation in slope-intercept form, which is expressed as y = mx + b, you need to follow these steps when provided with a slope (m) and a point (x, y).

For example, let’s say the slope (m) is 2 and the point given is (3, 4).

1. Use the point-slope formula: We can start with the point-slope form of the equation: y – y₁ = m(x – x₁). Here, (x₁, y₁) represents the point we have and m is the slope.
2. Plug in the values: Substituting m with 2 and the point (x₁, y₁) with (3, 4), we get: y – 4 = 2(x – 3).
3. Simplify the equation: Now, distribute the 2: y – 4 = 2x – 6.
4. Isolate y: Add 4 to both sides to solve for y. This gives us: y = 2x – 2.

Now, we have the equation in slope-intercept form: y = 2x – 2, which means the slope is 2 and the y-intercept is -2.