Question

If g(x) is a linear function such that g(-3)=2 and g(10= -4, find g(7)

Answer 1

Answer:

g(7) = -34/13

Step-by-step explanation:

In order to find g(7), we first need to find the g(x) function. To do so, use the two ordered pairs given, (-3, 2) and (10, -4). First we find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (2 - -4)/(-3 - 10)

m = 6/-13

Now that we have the slope, we can use that and either ordered pair in point-slope form to get the equation of the function.

y - y1 = m(x - x1)

y - 2 = 6/13(x + 3)

y - 2 = -6/13x - 18/13

y = -6/13x + 8/13

g(x) = 6/13x + 8/13

Now that we have this, we can plug in 7 for x and find g(7).

g(x) = -6/13x + 8/13

g(7) = -6/13(7) + 8/13

g(7) = -42/13 + 8/13

g(7) = -34/13