Question

step 4:
step 4: sketch the graph 1. draw a coordinate plane. 2. plot the points \\((4, 0)\\) and \\((0, -2)\\). 3. draw a straight line passing through both points.

sample answer:
the graph is a straight line passing through the x-axis at 4 and the y-axis at -2. it has a positive slope, rising 1 unit for every 2 units it moves to the right.

Explanation:

🆕 New Concept Discovered: Slope-Intercept Form
Rewriting linear equations to easily find the slope and starting point

Step 1: Identify the given equation

From the graph labels, we are given the linear equation in standard form:

$$ 2x - 4y = 8 $$

To find the equation of the line in the form \( y = \text{something} \), we need to isolate \( y \).

Step 2: Isolate the y-term

Subtract \( 2x \) from both sides of the equation:

$$ -4y = -2x + 8 $$

Step 3: Solve for y

Divide every term on both sides by \( -4 \):

$$ y = \frac{-2}{-4}x + \frac{8}{-4} $$

Simplify the fractions:

$$ y = \frac{1}{2}x - 2 $$

This matches the graph perfectly, showing a \( y \)-intercept at \( (0, -2) \) and a slope of \( m = \frac{1}{2} \).

Answer:

$$ y = \frac{1}{2}x - 2 $$