Question

On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 3, 0) and the y-axis at (0, 3). A straight blue line with a positive slope, labeled f of x, crosses the y-axis at (0, negative 3) and the x-axis at (1, 0). Both lines intersect at (3, 6).

Answer 1

f(6) = g(3)

Explanation:

Which statement is true regarding the functions on the graph?

f(6) = g(3)

f(3) = g(3)

f(3) = g(6)

f(6) = g(6)

Solution:

g(x) passes through the points (-3, 0) and the y-axis at (0, 3). The equation of g(x) is given as:

g(x) = y

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)`

`y-0=(3-0)/(0-(-3))(x-(-3))\\\\y=x+3\\\\g(x)=y= x+3\\\\g(x)=x+3`

f(x) passes through the points (0, -3) and the y-axis at (1, 0). The equation of f(x) is given as:

f(x) = y

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)`

`y-(-3)=(0-(-3))/(1-0)(x-0))\\\\y+3=x\\\\f(x)=y= x-3\\\\f(x)=x-3`

f(6) = x-3 = 6 - 3 = 3

g(3) = x + 3 = 3 + 3 = 3

f(6) = g(3)