Question

1. convert the following equation into \\(y=mx+b\\) form. state the slope and \\(y\\)-intercept.

\\4x-2y-8=0\\
slope is ____ \\(y\\)-intercept is ____

1. complete the table of values for each function.

a) function: \\(y=3x-2\\)
\

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline 5 & \\\\ \\hline 0 & \\\\ \\hline -7 & \\\\ \\hline \\end{tabular}$$

b) function: \\(y=-0.5x+5\\)
\

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline 5 & \\\\ \\hline 0 & \\\\ \\hline -7 & \\\\ \\hline \\end{tabular}$$

Explanation:

Convert equation to slope-intercept form

We start with the given linear equation:

$$4x - 2y - 8 = 0$$

To convert it into slope-intercept form \(y = mx + b\), we isolate \(y\):

$$-2y = -4x + 8$$

Divide both sides by \(-2\):

$$y = 2x - 4$$

Identify slope and y-intercept

From the slope-intercept form \(y = 2x - 4\):

• The slope \(m\) is the coefficient of \(x\), which is \(2\).
• The \(y\)-intercept \(b\) is the constant term, which is \(-4\).

Complete table for function a

The function is given as:

$$y = 3x - 2$$

We evaluate \(y\) for each given value of \(x\):

• For \(x = 5\):

$$y = 3(5) - 2 = 15 - 2 = 13$$

• For \(x = 0\):

$$y = 3(0) - 2 = -2$$

• For \(x = -7\):

$$y = 3(-7) - 2 = -21 - 2 = -23$$

Complete table for function b

The function is given as:

$$y = -0.5x + 5$$

We evaluate \(y\) for each given value of \(x\):

• For \(x = 5\):

$$y = -0.5(5) + 5 = -2.5 + 5 = 2.5$$

• For \(x = 0\):

$$y = -0.5(0) + 5 = 5$$

• For \(x = -7\):

$$y = -0.5(-7) + 5 = 3.5 + 5 = 8.5$$

Answer:

Question 3

• Equation in \(y = mx + b\) form: \(y = 2x - 4\)
• Slope: \(2\)
• y-intercept: \(-4\)

Question 4

a) Function: \(y = 3x - 2\)

\(x\)	\(y\)
\(0\)	\(-2\)
\(-7\)	\(-23\)

b) Function: \(y = -0.5x + 5\)

\(x\)	\(y\)
\(0\)	\(5\)
\(-7\)	\(8.5\)