Question

Write an equation in slope-intercept form of the line that passes through the points. $$ (-8.5,6.75),(3.33,-9.75) $$

Short answer

The equation of the line in slope-intercept form that passes through the points (-8.5,6.75) and (3.33,-9.75) is \(y = mx + b\) where \(m\) and \(b\) are the slope and y-intercept found in previous steps.

Step-by-step solution

Calculate the Slope

The slope \(m\) of a line passing through the points \((-8.5,6.75)\) and \((3.33,-9.75)\) is calculated as follows: \(m = \frac{y2 - y1}{x2 - x1} = \frac{-9.75 - 6.75}{3.33 - -8.5}\)

Calculate the y-intercept

Then the y-intercept \(b\) can be found using the formula \(b = y - mx\), using one of the given points, for example \((-8.5,6.75)\) and the calculated slope \(m\): \(b = 6.75 - m * -8.5\)

Write the Equation

Lastly, substitute the found values of \(m\) and \(b\) into the slope-intercept form of the line equation: \(y = mx + b\)