Question

Find the slope of the line that passes through the pair of points.(- 42.75,5.7) and (2.75, 4.1)Note: It didn't provide a graph or anything.The slope is __

Answer 1

A line equation can be written in slope-intercept form. The slope-intercept form is

`y=mx+b`

Where m represents the slope and b the y-intercept.

We can substitute our points on this form to get a system of equations to find the slope and y-intercept of our desired line. Using the points (- 42.75, 5.7) and (2.75, 4.1), we have

`\begin{cases}5.7=-42.75m+b \\ 4.1=2.75m+b\end{cases}`

If we subtract the second equation from the first equation, we get a new equation only for the slope.

`\begin{gathered} 5.7-(4.1)=-42.75m+b-(2.75m+b) \\ 1.6=-45.5m \\ m=-(1.6)/(45.5) \end{gathered}`

And this is our slope.