Question

which is the slope-intercept form of the equation of line $3x + 2y = 8$?
\\(\circ\\) $y = -\frac{3}{2}x + 4$
\\(\circ\\) $y = \frac{2}{3}x + 4$
\\(\circ\\) $y = \frac{3}{2}x - 4$
\\(\circ\\) $y = -\frac{3}{2}x - 4$

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We need to solve the equation \(3x+2y = 8\) for \(y\).

Step2: Isolate the \(y\) - term

Subtract \(3x\) from both sides of the equation \(3x + 2y=8\).
We get \(2y=-3x + 8\).

Step3: Solve for \(y\)

Divide each term in the equation \(2y=-3x + 8\) by \(2\).
\(y=\frac{-3x + 8}{2}=\frac{-3x}{2}+\frac{8}{2}\)
Simplify the fractions: \(y =-\frac{3}{2}x + 4\)

Answer:

\(y =-\frac{3}{2}x + 4\) (corresponding to the first option)