Question

1) Find the slope and y-intercept of the equation. Hint: Equation isn't in the correctformat to answer this question right away. Show all work and answer the question.- 4x + 8y = 30

Answer 1

Step-by-step explanation:

We are given the following linear equation:

`-4x+8y=30`

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;

`\begin{gathered} \text{For equation;} \\ Ax+By=C \\ A,B\text{ and C must be integers} \\ A\text{ must be positive} \end{gathered}`

The value of A in our equation is negative. We can now multiply all through by -1, and we'll have;

`\begin{gathered} (-4x)/(-1)+(8y)/(-1)=(30)/(-1) \\ 4x-8y=-30 \end{gathered}`

Subtract 4x from both sides;

`-8y=-30-4x`

Divide all through by -8;

`\begin{gathered} (-8y)/(-8)=(-30)/(-8)-(4x)/(-8) \\ y=3.75+(1)/(2)x \end{gathered}`

We can now refine this and re-write in the slope-intercept form;

`y=(1)/(2)x+3.75`

Now take note of the following.

For the equation given in slope-intercept form;

`y=mx+b`
`\begin{gathered} m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

Therefore;

ANSWER:

`\begin{gathered} \text{Slope}=(1)/(2) \\ y-\text{intercept}=3.75 \end{gathered}`