Question

directions: rewrite in slope-intercept form, then

1. $-2x + \frac{1}{2}y = -3$

equation:

slope y-intercept

coordinate plane graph

Explanation:

Step1: Isolate the y - term

We start with the equation \(-2x+\frac{1}{2}y = - 3\). First, we add \(2x\) to both sides of the equation to get the \(y\) - term by itself.
\(\frac{1}{2}y=2x - 3\)

Step2: Solve for y

To solve for \(y\), we multiply both sides of the equation by \(2\) (the reciprocal of \(\frac{1}{2}\)) to eliminate the fraction in front of \(y\).
\(y = 2\times(2x-3)\)
Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b=2x\), \(c=-3\)), we have \(y = 4x-6\)

The slope - intercept form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

For the equation \(y = 4x-6\), the slope \(m = 4\) and the \(y\) - intercept \(b=-6\)

Answer:

Equation: \(y = 4x-6\)
Slope: \(4\)
y - intercept: \(-6\)