Question

Converting from standard form to slope intercept form 3x+4y=4

Answer 1

Write out the given equation

`3x+4y=4`

Make y the subject of the equation given

`\begin{gathered} 3x+4y=4 \\ 3x-3x+4y=4-3x \\ 4y=4-3x \\ (1)/(4)*4y=(1)/(4)*4-(1)/(4)*3x \\ y=1-(3)/(4)x \end{gathered}`

Write the function of y in slope and intercept form defining the slope and intercept

`\begin{gathered} y=1-(3)/(4)x \\ y=-(3)/(4)x+1=====\text{equation}(1) \\ \text{the general equation of y in slope and intercept form is} \\ y=mx+c=====\text{equation}(2) \\ \text{where m is the slope and c is the intercept} \\ \text{Combining equation 1 and 2} \\ \text{From equation 1} \\ \text{slope(m)}=-(3)/(4) \\ i\text{ntercept(c)}=1 \end{gathered}`
`\begin{gathered} \text{the slope intercept form is} \\ y=-(3)/(4)x+1 \end{gathered}`

Hence, the slope-intercept form of the question is y= (-3/4)x +1