Question

Find the slope! Solve for y:7x+3y=217(0)+3y=210+3y=213y/3y=21/3Y=7(My answer)The correct answer was -7/3 What am I doing wrong?

Answer 1

To get the slope of this function, let's rewrite in the slope-intercept form.

The slope-intercept form have the following form:

`y=mx+b_{}`

where 'm' represents the slope and 'b' represents the y-intercept.

We have the following function

`7x+3y=21`

To rewrite in the slope-intercept form, we start with our original equation

`7x+3y=21`

Then, we can subtract '7x' from both sides:

`\begin{gathered} 7x+3y=21 \\ 7x+3y-7x=21-7x \\ 3y=21-7x \end{gathered}`

And then, finally, divide both sides by 3.

`\begin{gathered} 3y=21-7x \\ (3y)/(3)=(21-7x)/(3) \\ y=(21)/(3)-(7x)/(3) \\ y=7-(7x)/(3) \end{gathered}`

And with this, we have our final equation

`y=7-(7)/(3)x\Leftrightarrow y=-(7)/(3)x+7`

Done! If you compare this last equation with the general form of the line, you're going to find:

`\begin{cases}m=-(7)/(3) \\ b=7\end{cases}`

Where 'm' is the slope, and 'b' the y-intercept.