Answer
The space given to plot the graph on you attached image does not have (16, 0), so, we need to obtain another point to plot this.
Using the equation of the line, y = -0.25x + 4, we obtain another point on the line
When x = 8
y = -0.25x + 4
y = -0.25 (8) + 4
y = -2 + 4 = 2
So, a third point on the line is (8, 2)
Using the points (0, 4) and (8, 2), you can plot this graph.
Mark the point (0, 4) on the graph first. This is simply the point on the vertical line where 4 is located.
Then, mark the point (8, 2) on the graph. You will trace the point on the x-axis (horizontal axis) where 8 is located upwards to meet the line of y = 2 on the y-axis (vertical axis).
You will then connect the two points marked. This is the graph required.
So, the graph will look like
Step-by-step explanation
We are asked to plot the graph of y = -¼(x) + 4 or better written as
y = -0.25x + 4
To do this, we will use intercepts to get two points on the line and connect those two points to plot the graph
y = -0.25x + 4
When x = 0
y = -0.25x + 4
y = -0.25 (0) + 4
y = 0 + 4 = 4
First point on the line is (0, 4)
when y = 0
y = -0.25x + 4
0 = -0.25x + 4
0.25x = 4
Divide both sides by 0.25
(0.25x/0.25) = (4/0.25)
x = 16
Second point on the line is (16, 0)
So, connecting the two points (0, 4) and (16, 0).
The graph is shown under 'Answer'.
Hope this Helps!!!