Answer:
A) You want to see which of these functions is parallel to g and you give two points for g, (-4,6) and (4,2). Two linear functions are parallel if they share their slope but have a different x intercept. Then the first step is obtain the slope of g, this is : [tex]s =\frac{Y2 - Y1}{X2 - X1} = \frac{2 - 6}{4 - (-4)} = \frac{-4}{8} = \frac{-1}{2}[/tex]
So the correct answer is that with the slope equal to -1/2. This is the option c: y = -1/2x - 1 and you can see that when x = 0, the first therm anulates and y = -1, so the function passes through the point (0, -1)
B) If the slope is 0, then our function is y = 0*x + b = b. And we want it to pass through the point (6, -8). In standard notation a pair is represented as (x,y), so y must value -8 when x values 6.
Then the function that pasese trough the point ia y(x) = -8. (the equation x(y) = 6 also passes through the point (6, - 8) but in this case the slope is not 0) So the correct option is D.
C) Now we want to find the equation that pases trough the point (1,24) and has a slope of -0.6
all the functions are in the form of : 3x + 5y = c, where c changes in every option, then:
y = c/5 - 3/5X = c/5 - 0.6x
So all the options have slope of -0.6, then we now need to see which option passes through the point (1,24), and replacing this pair in the equation, we get:
24 = c/5 - 0.6*1
c/5 = 24 + 0.6
c = 24.6 = 123
So the correct answer is that with C equal to 123, wich is the option C.
