Let me work through this problem step by step.
Step 1: Rewrite the equation in slope-intercept form (y = mx + b)
Starting with: 6x - 2y = 8
I need to solve for y:
- First, subtract 6x from both sides: -2y = -6x + 8
- Then divide everything by -2: y = (-6x)/(-2) + 8/(-2)
- Simplify: y = 3x - 4
So the equation in slope-intercept form is:
y = 3x - 4
Step 2: Identify the slope
In the form y = mx + b, the coefficient of x (which is m) represents the slope.
Looking at y = 3x - 4, the number multiplying x is 3.
So the slope is:
3
Step 3: What does the slope mean?
The slope tells us how steep the line is and which direction it goes. A slope of 3 means that for every 1 unit you move to the right on the graph, you go up 3 units. It's a positive slope, so the line rises as you go from left to right.
Let me verify my calculation one more time:
- Original: 6x - 2y = 8
- Subtract 6x: -2y = -6x + 8
- Divide by -2: y = 3x - 4 ✓
This is correct!
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Final Answer:
1. The equation in slope-intercept form is:
y = 3x - 4
2. The slope is:
3
3. The slope means that for every 1 unit you move to the right, the line goes up 3 units. It shows the rate of change or steepness of the line.
Parent Tip: Review the logic above to help your child master the concept of rewriting equations in slope intercept form worksheet.
