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Mathematics , 17.02.2022 19:25

A linear function that represents the number of animals adopted from the shelter is compared to a different linear function that represents the hours volunteers work at the shelter each week. Describe the key features of the functions that are needed to determine if these lines intersect.

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The slopes of the equations must be different:

y1= a*x + b

y2 = c*x + b

then a ≠ c

Step-by-step explanation:

A linear function is:

Y = a*x + b

now, suppose we have other linear function

H = c*x + d

Let's find the condition needed to have an intersection of these two lines, or:

a*x + b = c*x + d

(a - c)*x = d - b

Where a, c, d and b are real numbers.

You can see that the only condition is that the coefficient that multiplicates the variable (x) must be different than 0 (because if it is 0, the x vanishes and we can never solve the equation)

So we must have that the slopes of the two linear equations need to be different.

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