Question

x + 2y = 6
$y = -\frac{1}{2}x + 3$
click to select points on the graph.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and axes labeled.)

Explanation:

To graph the line \( y = -\frac{1}{2}x + 3 \) (which is equivalent to \( x + 2y = 6 \) after rearranging), we can find two points on the line:

Step 1: Find the y - intercept

The equation is in slope - intercept form \( y=mx + b \), where \( b \) is the y - intercept. For \( y = -\frac{1}{2}x+3 \), when \( x = 0 \):
\( y=-\frac{1}{2}(0)+3=3 \)
So one point is \( (0, 3) \).

Step 2: Find another point using the slope

The slope \( m=-\frac{1}{2} \), which means for every 2 units we move to the right (increase \( x \) by 2), we move down 1 unit (decrease \( y \) by 1). Starting from \( (0, 3) \):
If \( x = 2 \), then \( y=-\frac{1}{2}(2)+3=- 1 + 3=2 \)
So another point is \( (2, 2) \). (We could also use the x - intercept: set \( y = 0 \), then \( 0=-\frac{1}{2}x + 3\), \( \frac{1}{2}x=3 \), \( x = 6 \), so \( (6, 0) \) is also a point on the line.)

To graph the line, plot the points \( (0, 3) \) and \( (2, 2) \) (or \( (6, 0) \)) on the coordinate plane and draw a straight line through them.

If you were asked to identify the relationship between \( x + 2y = 6 \) and \( y=-\frac{1}{2}x + 3 \), they are equivalent (the second is the solved - for - \( y \) form of the first).

If you need to graph the line, the key points to plot are \( (0, 3) \) (y - intercept) and \( (6, 0) \) (x - intercept, found by setting \( y = 0 \) in \( x+2y = 6\): \( x+2(0)=6\Rightarrow x = 6 \)) or other points calculated using the slope.

Answer:

To graph the line \( y = -\frac{1}{2}x + 3 \) (which is equivalent to \( x + 2y = 6 \) after rearranging), we can find two points on the line:

Step 1: Find the y - intercept

The equation is in slope - intercept form \( y=mx + b \), where \( b \) is the y - intercept. For \( y = -\frac{1}{2}x+3 \), when \( x = 0 \):
\( y=-\frac{1}{2}(0)+3=3 \)
So one point is \( (0, 3) \).

Step 2: Find another point using the slope

The slope \( m=-\frac{1}{2} \), which means for every 2 units we move to the right (increase \( x \) by 2), we move down 1 unit (decrease \( y \) by 1). Starting from \( (0, 3) \):
If \( x = 2 \), then \( y=-\frac{1}{2}(2)+3=- 1 + 3=2 \)
So another point is \( (2, 2) \). (We could also use the x - intercept: set \( y = 0 \), then \( 0=-\frac{1}{2}x + 3\), \( \frac{1}{2}x=3 \), \( x = 6 \), so \( (6, 0) \) is also a point on the line.)

To graph the line, plot the points \( (0, 3) \) and \( (2, 2) \) (or \( (6, 0) \)) on the coordinate plane and draw a straight line through them.

If you were asked to identify the relationship between \( x + 2y = 6 \) and \( y=-\frac{1}{2}x + 3 \), they are equivalent (the second is the solved - for - \( y \) form of the first).

If you need to graph the line, the key points to plot are \( (0, 3) \) (y - intercept) and \( (6, 0) \) (x - intercept, found by setting \( y = 0 \) in \( x+2y = 6\): \( x+2(0)=6\Rightarrow x = 6 \)) or other points calculated using the slope.