Question

Use algebra to find the point at which the line h(x)=−(3/5)x+(7/5) intersects the line k(x)=(−8/3)x+(404/45).

Answer 1

Answer: the point (3.667, 0.8)

Step-by-step explanation:

We want to find the point at which the lines:

h(x) = -(3/5)*x + (7/5)

and

k(x) = (-8/3)*x + (404/45)

If the lines intersect, then we must have:

h(x) = k(x)

if we write the functions we get:

-(3/5)*x + (7/5) = (-8/3)*x + (404/45)

Now we need to solve this for x.

-(3/5)*x + (8/3)*x = (404/45) - (7/5)

(8/3 - 3/5)*x = 404/45 - 63/45 = 341/45

(40/15 - 9/15)*x = 341/45

(31/15)*x = 341/45

x = (341/45)*(15/31) = 3.667

Now we can input this value of x in the functions to get the output.

h(3.667) = -(3/5)*3.667 + 7/5 = -0.8

Then the point where our points intersect is the point (3.667, 0.8)