Question

Using algebra, find the point at which the line

f(x)=1.3x+3.09 intersects the line
h(x)=4.4x+10.22. Write the values of
y in decimal form.

A) The point of intersection is (2.67, 14.02).
B) The point of intersection is (3.00, 13.73).
C) The point of intersection is (4.09, 10.22).
D) The point of intersection is (1.20, 15.31).

Answer 1

To find the point of intersection between the two lines, solve their equations simultaneously. The point of intersection is approximately (-3.397, -0.06).

Step-by-step explanation:

To find the point of intersection between the two lines, we need to solve their equations simultaneously. The given equations are f(x) = 1.3x+3.09 and h(x) = 4.4x+10.22. Setting the two equations equal, we have 1.3x+3.09 = 4.4x+10.22.

Now, we can solve for x: subtracting 1.3x from both sides gives 3.09 = 3.1x+10.22, and then subtracting 10.22 from both sides gives -7.13 = 2.1x. Dividing both sides by 2.1, we find that x ≈ -3.397.

Finally, substituting this value of x back into one of the original equations, we can find the corresponding y-coordinate. Using the equation f(x) = 1.3x+3.09, we have f(-3.397) = 1.3(-3.397)+3.09 ≈ -0.06. Therefore, the point of intersection is approximately (-3.397, -0.06).