Final answer:
The point at which the line f(x) = - 4x + 8 intersects the line g(x) = 52 - 10 is (-8.5, 42). To find this, set the two equations equal to each other, solve for x, then substitute x back into either original equation to find the corresponding y-value.
Step-by-step explanation:
To find the point of intersection between the two lines f(x) = -4x + 8 and g(x) = 52 - 10 (which simplifies to g(x) = 42), we first set the equations equal to each other:
-4x + 8 = 42
Next, solve for x by first subtracting 8 from each side:
-4x = 42 - 8
-4x = 34
Then, divide each side by -4:
x = 34 / -4
x = -8.5
After finding the x-value, you can plug it back into either of the original equations to find the y-value. In this case, let's use f(x) = -4x + 8:
f(-8.5) = -4(-8.5) + 8
f(-8.5) = 34 + 8
f(-8.5) = 42
So, the point at which the two lines intersect is (-8.5, 42).
Learn more about Line Intersection