Question

2) Explain the steps on how you would write x + 2y < 8 in slope intercept form.

Answer 1

ANSWER

$y\leqslant-\frac{1}{2}x+4$

EXPLANATION

The slope-intercept form of a line is,

$y=mx+b$

In this case, we have an inequality but the steps to rewrite it in the slope-intercept form are similar to the ones we would use if we had an equality.

Step 1: subtract x from both sides of the inequality,

$\begin{gathered} x-x+2y\le8-x \\ \\ 2y\le-x+8 \end{gathered}$

Step 2: divide both sides by 2,

$\begin{gathered} \frac{2y}{2}\le\frac{-x+8}{2} \\ \\ y\le\frac{-x+8}{2} \end{gathered}$

Step 3: distribute the denominator and simplify the fractions if possible,

$\begin{gathered} y\le\frac{-x}{2}+\frac{8}{2} \\ \\ y\le-\frac{1}{2}x+4 \end{gathered}$

Hence, the inequality in slope-intercept form is,

$y\leqslant-\frac{1}{2}x+4$