Find a linear function g,g(3)= - 5 and g(7)= -1?

Question

a) find an equation for g
b) find g(-2)
c) find a such that g(a) = 75.....

would it be.... -5 - (-1) divided by 3-7 which then turns into -3/2 which I can come up with the equation g = -3/2x - 1/2 for a)? I'm so confused... gave it my best shot.

Answer 1

this means you have two points
(3, -5) and (7, -1)
The slope between these two points is:
(-5 - - 1)/(3 - 7) = -4/-4 = 1
pick a point (I'll use the first one)
y - y1 = m(x - x1)
y - -5 = 1(x - 3)
y + 5 = x - 3
y = x - 3 - 5
y = x - 8
so g(x) = x - 8

So then g(-2) = -2 - 8 = -10
g(a) = 75, so x - 8 = 75 so x = 75 + 8
x = 83

Anytime they give you two points, you can use this method
Take the points, calculate slope, find the equation of the line, then solve for other points.

This won't work if it is not a linear function, however.

Answer 2

in simple terms positioned: almost no one receives through existence without falling out of grace at cases. If we were to be judged in accordance to the regulation, very few would not struggle through a lot in justice. through Christ, one might want to wish for mercy previous what the regulation might want to require. Having lived a existence right here on earth Jesus knows what that's favor to be powerless. at the same time with his blood he has offered the right to forgive sins. In Jesus Christ mercy has triumphed over justice!