Question

click to select points on the graph
x + 2y = 6
$y = -\frac{1}{2}x + 3$

Explanation:

Step1: Find x-intercept (y=0)

For \( x + 2y = 6 \), set \( y = 0 \):
\( x + 2(0) = 6 \)
\( x = 6 \). So point is \( (6, 0) \).

For \( y = -\frac{1}{2}x + 3 \), set \( y = 0 \):
\( 0 = -\frac{1}{2}x + 3 \)
\( \frac{1}{2}x = 3 \)
\( x = 6 \). Same point \( (6, 0) \).

Step2: Find y-intercept (x=0)

For \( x + 2y = 6 \), set \( x = 0 \):
\( 0 + 2y = 6 \)
\( y = 3 \). Point: \( (0, 3) \).

For \( y = -\frac{1}{2}x + 3 \), set \( x = 0 \):
\( y = -\frac{1}{2}(0) + 3 = 3 \). Same point \( (0, 3) \).

Step3: Find another point (e.g., x=2)

For \( x + 2y = 6 \), \( x = 2 \):
\( 2 + 2y = 6 \)
\( 2y = 4 \)
\( y = 2 \). Point: \( (2, 2) \).

For \( y = -\frac{1}{2}x + 3 \), \( x = 2 \):
\( y = -\frac{1}{2}(2) + 3 = -1 + 3 = 2 \). Same point \( (2, 2) \).

The two equations represent the same line. To graph, plot points like \( (0, 3) \), \( (6, 0) \), \( (2, 2) \) and draw a straight line through them.

Answer:

The two equations are equivalent (represent the same line). Key points to plot: \( (0, 3) \), \( (6, 0) \), \( (2, 2) \) (or others), then draw the line.