Question

name
1 match each equation with the slope and y - intercept of the line it represents.
equation\tslope and y - intercept
$y = - 3x+\frac{1}{2}$\tslope $- 3$ and y - intercept $\frac{1}{2}$
$y=\frac{1}{2}x - 3$\tslope $0$ and y - intercept $1$
$y = 1x$\tslope $\frac{1}{2}$ and y - intercept $- 3$
$y = 1$\tslope $1$ and y - intercept $0$
for problems 2 - 5, graph the equation.

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

Explanation:

Step1: Recall slope - intercept form

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

Step2: Analyze equation \(y=\frac{1}{2}x - 2\)

For the equation \(y=\frac{1}{2}x-2\), comparing with \(y = mx + b\), we can see that the slope \(m=\frac{1}{2}\) and the \(y\) - intercept \(b=- 2\).

Step3: Analyze equation \(y = 3x+2\)

For the equation \(y = 3x + 2\), comparing with \(y=mx + b\), we can see that the slope \(m = 3\) and the \(y\) - intercept \(b = 2\).

Answer:

For \(y=\frac{1}{2}x - 2\): \(m=\frac{1}{2}\), \(b=-2\)

For \(y = 3x+2\): \(m = 3\), \(b = 2\)