what is the x intercept of the equation y minus 1 over 4x +1

To find the x-intercept of an equation, we set \( y = 0 \) and solve for \( x \). Given the equation:

\[
y - 1 = \frac{1}{4x + 1}
\]

### Step 1: Set \( y = 0 \)
\[
0 - 1 = \frac{1}{4x + 1}
\]
This simplifies to:
\[
-1 = \frac{1}{4x + 1}
\]

### Step 2: Solve for \( x \)
Multiply both sides by \( 4x + 1 \) to eliminate the denominator:
\[
-1 \cdot (4x + 1) = 1
\]
\[
-(4x + 1) = 1
\]
\[
-4x - 1 = 1
\]

Add 1 to both sides:
\[
-4x = 2
\]

Now, divide by -4:
\[
x = -\frac{1}{2}
\]

Thus, the x-intercept is \( x = -\frac{1}{2} \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. What is the y-intercept of the equation \( y - 1 = \frac{1}{4x + 1} \)?
2. How do you find the slope of this equation?
3. What happens to the x-intercept if the equation is multiplied by a constant?
4. How do you determine if the graph of this equation is linear or nonlinear?
5. What is the domain and range of this equation?

**Tip:** Always double-check that the equation is in a solvable form before finding intercepts!

What is the x intercept of the equation y minus 1 over 4x + 1?

Discover how to solve for the x-intercept of the equation y - 1 = 1 / (4x + 1) through detailed step-by-step instructions. This problem explores algebraic concepts such as solving rational equations and finding intercepts. Ideal for students in Grades 9-11.

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