using algebra, find the point at which the line g(x)=-4x+8 intersects the line K(x)=5x-10

To find the point of intersection of the two lines, we need to set their equations equal to each other because, at the point of intersection, the \( y \)-values (or \( g(x) \) and \( K(x) \)) are equal.

Given:
- \( g(x) = -4x + 8 \)
- \( K(x) = 5x - 10 \)

Set them equal to each other:
\[
-4x + 8 = 5x - 10
\]

### Step 1: Solve for \( x \)
Move all terms involving \( x \) to one side and constants to the other side:
\[
-4x - 5x = -10 - 8
\]
\[
-9x = -18
\]

Now, divide both sides by \(-9\):
\[
x = 2
\]

### Step 2: Solve for \( y \)
Now that we have \( x = 2 \), substitute it back into either equation to find \( y \). Let's use \( g(x) = -4x + 8 \):

\[
g(2) = -4(2) + 8 = -8 + 8 = 0
\]

So, the point of intersection is \( (2, 0) \).

### Final Answer:
The lines \( g(x) = -4x + 8 \) and \( K(x) = 5x - 10 \) intersect at the point \( (2, 0) \).

Would you like more details on any step or further clarifications?

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Here are 5 related questions:
1. How do you find the slope of a line given its equation?
2. What does the slope represent in the context of a line's graph?
3. Can two lines intersect at more than one point? Why or why not?
4. What is the significance of parallel lines in a system of equations?
5. How would the method change if the lines were curves instead?

**Tip:** When solving for the intersection of two lines, always look for equal values in their equations, since this represents a common point.

Using algebra, find the point at which the line g(x)=-4x+8 intersects the line K(x)=5x-10.

Discover how to find the intersection point of the lines g(x) = -4x + 8 and K(x) = 5x - 10 using algebra. This step-by-step solution explains the process of solving a system of linear equations, suitable for students in Grades 8-10.

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