Problem 1)
The function f(x) = (-1/4)x-2 is the same as y = (-1/4)x-2 where y = f(x).
This is a linear equation in the form y = mx+b
m = -1/4 is the slope
b = -2 is the y intercept
To graph this equation, we start off at the y intercept -2. This s the point (0,-2). In other words, it is at -2 on the vertical y axis number line.
Then we move to the point (4,-3) after moving down 1 and over to the right 4. This is because
slope = rise/run = -1/4
rise = -1
run = 4
The negative rise value indicates we go down instead of up.
Once you have the two points (0,-2) and (4,-3) plotted, draw a straight line through them. See figure 1 in the attached images.
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Problem 2)
Start with the graph of y = |x| as the parent function. This is a V shaped function that is basically composed of two lines joined together at the vertex (0,0). The line on the left goes through (-1,1) and (0,0). The line on the right goes through (0,0) and (1,1). The parent function is shown in blue in figure 2 (see attached).
Shift the parent function 6 units to the right and then 4 units down to go from |x| to |x-6|-4. This new graph is marked in red on the same figure 2, which is the final answer.
