Question

iv. graph each of the equations:

1. $2x + y = 6$
2. $2y = x - 2$
3. $y = -1$

Explanation:

For Equation 10: \( 2x + y = 6 \)

Step1: Find Intercepts

To graph \( 2x + y = 6 \), find x - intercept (set \( y = 0 \)):
\( 2x+0 = 6\Rightarrow x = 3 \). So point is \( (3,0) \).
Find y - intercept (set \( x = 0 \)):
\( 0 + y=6\Rightarrow y = 6 \). So point is \( (0,6) \).

Step2: Plot and Draw

Plot \( (3,0) \) and \( (0,6) \) on the grid, then draw a line through them.

For Equation 11: \( 2y = x - 2 \)

Step1: Rewrite in Slope - Intercept Form

Solve for \( y \): \( y=\frac{1}{2}x - 1 \).
Slope \( m=\frac{1}{2} \), y - intercept \( b=-1 \) (point \( (0, - 1) \)).

Step2: Find Another Point

Using slope (rise 1, run 2), from \( (0,-1) \), move 1 up and 2 right to get \( (2,0) \).

Step3: Plot and Draw

Plot \( (0,-1) \) and \( (2,0) \), then draw a line through them.

For Equation 12: \( y=-1 \)

Step1: Identify Line Type

\( y = - 1 \) is a horizontal line (since y - value is constant) passing through all points with \( y=-1 \).

Step2: Plot and Draw

Find points like \( (0,-1) \), \( (1,-1) \), \( (2,-1) \) (any x, \( y = - 1 \)), plot them and draw a horizontal line.

Answer:

(Graphing Steps Summary):

• For \( 2x + y = 6 \): Plot \( (3,0) \) and \( (0,6) \), draw line.
• For \( 2y = x - 2 \): Plot \( (0,-1) \) and \( (2,0) \), draw line.
• For \( y=-1 \): Draw horizontal line through \( y = - 1 \) (e.g., \( (0,-1),(1,-1),\dots \)).