Question

1. draw the graph of linear function $y = \frac{1}{2}x + 1$.

$x$	$y$
-2
-1
0
1
4

(coordinate system with y-axis from -5 to 5, x-axis from -5 to 0 shown)

1. draw the graph of linear function $y = -\frac{1}{2}x + 1$.

$x$	$y$
-1
0
1
2
4

(coordinate system with y-axis from -5 to 5, x-axis from -5 to 0 shown)

Explanation:

Problem 3

Step1: Calculate y for x=-4

$y=\frac{1}{2}(-4)+1=-2+1=-1$

Step2: Calculate y for x=-2

$y=\frac{1}{2}(-2)+1=-1+1=0$

Step3: Calculate y for x=-1

$y=\frac{1}{2}(-1)+1=-0.5+1=0.5$

Step4: Calculate y for x=0

$y=\frac{1}{2}(0)+1=0+1=1$

Step5: Calculate y for x=1

$y=\frac{1}{2}(1)+1=0.5+1=1.5$

Step6: Calculate y for x=4

$y=\frac{1}{2}(4)+1=2+1=3$

Step7: Plot points and draw line

Plot the calculated (x,y) pairs and connect with a straight line.

Problem 4

Step1: Calculate y for x=-4

$y=-\frac{1}{2}(-4)+1=2+1=3$

Step2: Calculate y for x=-1

$y=-\frac{1}{2}(-1)+1=0.5+1=1.5$

Step3: Calculate y for x=0

$y=-\frac{1}{2}(0)+1=0+1=1$

Step4: Calculate y for x=1

$y=-\frac{1}{2}(1)+1=-0.5+1=0.5$

Step5: Calculate y for x=2

$y=-\frac{1}{2}(2)+1=-1+1=0$

Step6: Calculate y for x=4

$y=-\frac{1}{2}(4)+1=-2+1=-1$

Step7: Plot points and draw line

Plot the calculated (x,y) pairs and connect with a straight line.

Answer:

x	y
-2	0
-1	0.5
0	1
1	1.5
4	3

(Graph: Plot points (-4,-1), (-2,0), (-1,0.5), (0,1), (1,1.5), (4,3) and draw a straight line through them.)