Question
Find the \( x \)-intercept of the following line. \[ y=-\frac{9}{4} x-1 \] Enter the answer as ordered pair \( (x, y) \).
Ask by Black Osborne. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The \( x \)-intercept is at \( \left( -\frac{4}{9}, 0 \right) \).
Solution
To find the \( x \)-intercept of the line given by the equation:
\[
y = -\frac{9}{4}x - 1
\]
the \( x \)-intercept occurs where \( y = 0 \).
Set \( y \) to 0 and solve for \( x \):
\[
0 = -\frac{9}{4}x - 1
\]
Add 1 to both sides:
\[
\frac{9}{4}x = -1
\]
Multiply both sides by \( \frac{4}{9} \):
\[
x = -\frac{4}{9}
\]
Therefore, the \( x \)-intercept is at the point \( \left( -\frac{4}{9}, 0 \right) \).
**Answer:** \(\left( -\dfrac{4}{9},\ 0 \right)\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the \( x \)-intercept of the line given by the equation \( y = -\frac{9}{4} x - 1 \), we need to set \( y \) to 0 and solve for \( x \). Setting \( y \) to 0: \[ 0 = -\frac{9}{4} x - 1 \] Now, add 1 to both sides: \[ 1 = -\frac{9}{4} x \] Next, multiply both sides by \(-\frac{4}{9}\) to isolate \( x \): \[ x = -\frac{4}{9}(1) = -\frac{4}{9} \] So, the \( x \)-intercept is the ordered pair: \[ \left(-\frac{4}{9}, 0\right) \]
