` ` To write an equation in slope intercept form (y=mx + b) for the line that passes through the points (0, -2) and (4, 2), we must find determine the slope and y-intercept of the line.
Slope (m) is defined as the steepness of the line and can be written as the ratio of the line's rise over its run. The formula is `(y_(2)-y_(1))/(x_(2)-x_(1)).`` `
` `By substituting the x and y values from the ordered pairs into the formula and simplifying as shown, we can determine the slope if the line passing through these points is 1. Therefore, m = 1.
The y-intercept (b) is the point where the line crosses the y-axis on the coordinate plane. This point will always be (0, y). Since one of the points given to us is in this form, we already know the y-intercept is -2.
To verify this, use the point-slope formula.
Choose one of the points to substitute in for the `y_(1)` and `x_(1)` and use the slope you found in the previous step to substitute in for `m`. Then simplify and solve for y.
`(y-2) = 1(x-4)`
`(y-2) = x -4 `
`y = x - 2`
This is the equation of the line in slope intercept form. We know the slope of the line is 1 and this equation confirms for us that the y-intercept is -2.