I need help with figuring out linear functions
1 answer:
Answer:
see explanation
Step-by-step explanation:
Part 1
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 80) and (x₂, y₂ ) = (2, 110) ← 2 points from the table
m = = 30
Given the point (0, 50 ) ⇒ c = 50
D(g) = 30g + 50 ← linear equation
A
D(6.5) = (30 × 6.5) + 50 = 195 + 50 = 245
B
D(4.25) = (30 × 4.25) + 50 = 127.5 + 50 = 177.5
C
D(50) = (30 × 50) + 50 = 1500 + 50 = 1550
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Since x can't be zero (it sits at the denominator of the left hand side), let's split cases:
If x is positive
It this case, we can multiply both sides by x without changing the inequality sign:
But since we're assuming that x is positive, we can only accept the numbers between 0 and 1.
If x is negative
It this case, in order to multiply both sides by x we have to change the inequality sign:
But since we're assuming that x is negative, we can only accept the numbers which are smaller than -1.
So, putting all the pieces together, we have that the solution is given by the following interval: