Question

On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 6, 0) and the y-axis at (0, 6). A straight blue line with a negative slope, labeled f of x, crosses the x-axis at (negative 0.75, 0) and the y-axis at (0, negative 2).
f(4) = g(4)
f(4) = g(–2)
f(2) = g(–2)
f(–2) = g(–2)

Answer 1

First find the equations.

g passes through (-6,0) and (0,6) so slope = (6-0)/(0-(-6)) = 1, hence g(x) = x + 6.

f passes through (-0.75,0) and (0,-2) so slope = (-2-0)/(0-(-0.75)) = -2/0.75 = -8/3, hence f(x) = (-8/3)x - 2.

Evaluate and compare:

- g(4) = 4 + 6 = 10; f(4) = (-8/3)*4 - 2 = -38/3 ≈ -12.67 → f(4) ≠ g(4).
- g(-2) = -2 + 6 = 4; f(4) = -38/3 ≠ 4 → f(4) ≠ g(-2).
- f(2) = (-8/3)*2 - 2 = -22/3 ≈ -7.33, which ≠ g(-2)=4 → f(2) ≠ g(-2).
- f(-2) = (-8/3)*(-2) - 2 = 10/3 ≈ 3.33, which ≠ g(-2)=4 → f(-2) ≠ g(-2).

Conclusion: none of the given equalities are true.