EXPLANATION:
We are given the following linear equation:
[tex]-4x+8y=30[/tex]
Take note that this is an equation in the STANDARD FORM.
For an equation in the standard form, two main conditions must be satisfied and these are;
[tex]\begin{gathered} \text{For equation;} \\ Ax+By=C \\ A,B\text{ and C must be integers} \\ A\text{ must be positive} \end{gathered}[/tex]
The value of A in our equation is negative. We can now multiply all through by -1, and we'll have;
[tex]\begin{gathered} \frac{-4x}{-1}+\frac{8y}{-1}=\frac{30}{-1} \\ 4x-8y=-30 \end{gathered}[/tex]
Subtract 4x from both sides;
[tex]-8y=-30-4x[/tex]
Divide all through by -8;
[tex]\begin{gathered} \frac{-8y}{-8}=\frac{-30}{-8}-\frac{4x}{-8} \\ y=3.75+\frac{1}{2}x \end{gathered}[/tex]
We can now refine this and re-write in the slope-intercept form;
[tex]y=\frac{1}{2}x+3.75[/tex]
Now take note of the following.
For the equation given in slope-intercept form;
[tex]y=mx+b[/tex][tex]\begin{gathered} m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]
Therefore;
ANSWER:
[tex]\begin{gathered} \text{Slope}=\frac{1}{2} \\ y-\text{intercept}=3.75 \end{gathered}[/tex]
