Matched Problem 4.4 - Find the x- and y-intercepts of the function 2y = x + 6 where -6 < x ≤ 2 and sketch its graph using the intercepts.
( Please give an explanation for your answer since there's no explanation in the picture I attached as to why and how -1 turned into -4 ).
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Answer:
Find the x-intercept/Zero:
2y = x + 6
To solve for the x-intercept, substitute y as 0.
2(0) = x + 6
Any number multiplied by zero is always zero.
0 = x + 6
Move 6 to the left-hand side and change its sign.
-6 = x
Swap the sides.
x = -6
Find the y-intercept:
2y = x + 6
To solve for the y-intercept, substitute x as 0.
2y = 0 + 6
Simplify.
2y = 6
Divide both sides by 2.
y = 3
Find the points:
-6 < x ≤ 2
Substitute x as values from -6 to 2 into the equation.
2y = -6 + 6
2y = -5 + 6
2y = -4 + 6
2y = -3 + 6
2y = -2 + 6
2y = -1 + 6
2y = 0 + 6
2y = 1 + 6
2y = 2 + 6
Solve for y.
y = 0
y = ½
y = 1
y = 3/2
y = 2
y = 5/2
y = 3
y = 7/2
y = 4
Rewrite as ordered pairs.
(-6, 0), (-5, ½), (-4, 1), (-3, 3/2), (-2, 2), (-1, 5/2), (0, 3), (1, 7/2), (2, 4)
Since -6 < x ≤ 2, (-6, 0) is an excluded point, when graphing, do not fully shade the point (-6, 0), instead, draw a circle at that point just like how it is at the image (the excluded point in the example is (6, -1))
Please give an explanation for your answer since there's no explanation in the picture I attached as to why and how -1 turned into -4.
I presume that is just an error committed by the writer of the handout.