Solve 7y = 154 - 11x- Quick Guide to Finding the Slope
What You're Actually Solving Here
The equation 7y = 154 - 11x looks messy. Two variables, a big number, a negative coefficient. Most students freeze up. Don't.
You're being asked to put this in a usable form so you can identify the slope and y-intercept. That's it. One quick algebraic move and you're done.
Step 1: Get y By Itself
Right now, y is trapped. It has a coefficient of 7. Free it by dividing both sides by 7.
7y ÷ 7 = (154 - 11x) ÷ 7
y = 22 - (11/7)x
You can rewrite that as:
y = -(11/7)x + 22
That right there is slope-intercept form: y = mx + b
Finding the Slope
The slope is the number directly in front of x. In this case:
The slope is -11/7
That's approximately -1.57. The negative sign means the line slopes downward from left to right.
What the Slope Actually Tells You
For every 7 units you move right on the x-axis, the line drops 11 units. That's a moderately steep decline. Not vertical, not flat. Just... downhill.
Getting Started: The Complete Process
- Start with 7y = 154 - 11x
- Divide every term by 7
- Simplify: y = -(11/7)x + 22
- Identify the slope: m = -11/7
- Identify the y-intercept: b = 22
That's the entire process. No tricks, no hidden steps.
Quick Reference: Equation Forms Compared
| Form | Equation | What You Read |
|---|---|---|
| Standard | Ax + By = C | The starting point, before isolating y |
| Slope-Intercept | y = mx + b | Slope (m) and y-intercept (b) are visible |
| Point-Slope | y - y₁ = m(x - x₁) | Used when you know a point and the slope |
Your original equation was in standard form. Converting to slope-intercept form is how you extract the slope.
Common Mistakes to Skip
- Dividing only one term by 7 — you must divide every term on the right side
- Forgetting the negative sign — the slope is negative, not positive
- Rounding too early — keep fractions as fractions until the final answer if precision matters
The Answer, Plain and Simple
Slope of 7y = 154 - 11x is -11/7. Y-intercept is 22.
Write it as y = -(11/7)x + 22 and you're finished. That's all this problem requires.