Find the x- and y-intercepts of the graph of the equation algebraically. 4x – 9y = 16 x-intercept (x, y) = (| y-intercept (x, y) =(| , Y) =|

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Finding the x- and y-intercepts of the Graph of an Equation**

To find the x- and y-intercepts of the graph of the given equation algebraically, follow these steps:

**Equation:**
\[ 4x - 9y = 16 \]

**x-intercept:**
The x-intercept is the point where the graph crosses the x-axis. At this point, \( y = 0 \). Substitute \( y = 0 \) into the equation to find the x-intercept.

\[ 4x - 9(0) = 16 \]

Thus,

\[ 4x = 16 \]

Solving for \( x \),

\[ x = \frac{16}{4} \]
\[ x = 4 \]

Therefore, the x-intercept is \( (x, y) = (4, 0) \).

**y-intercept:**
The y-intercept is the point where the graph crosses the y-axis. At this point, \( x = 0 \). Substitute \( x = 0 \) into the equation to find the y-intercept.

\[ 4(0) - 9y = 16 \] 

Thus,

\[ -9y = 16 \]

Solving for \( y \),

\[ y = \frac{16}{-9} \]
\[ y = -\frac{16}{9} \]

Therefore, the y-intercept is \( (x, y) = (0, -\frac{16}{9}) \).

So, we have:
**x-intercept:**
\[ (x, y) = (4, 0) \]

**y-intercept:**
\[ (x, y) = (0, -\frac{16}{9}) \]

Here are the steps in summary form:
1. To find the x-intercept, set \( y = 0 \) and solve for \( x \).
2. To find the y-intercept, set \( x = 0 \) and solve for \( y \).

These intercepts are crucial for graphing linear equations and understanding their intersections with the axes.
Transcribed Image Text:**Finding the x- and y-intercepts of the Graph of an Equation** To find the x- and y-intercepts of the graph of the given equation algebraically, follow these steps: **Equation:** \[ 4x - 9y = 16 \] **x-intercept:** The x-intercept is the point where the graph crosses the x-axis. At this point, \( y = 0 \). Substitute \( y = 0 \) into the equation to find the x-intercept. \[ 4x - 9(0) = 16 \] Thus, \[ 4x = 16 \] Solving for \( x \), \[ x = \frac{16}{4} \] \[ x = 4 \] Therefore, the x-intercept is \( (x, y) = (4, 0) \). **y-intercept:** The y-intercept is the point where the graph crosses the y-axis. At this point, \( x = 0 \). Substitute \( x = 0 \) into the equation to find the y-intercept. \[ 4(0) - 9y = 16 \] Thus, \[ -9y = 16 \] Solving for \( y \), \[ y = \frac{16}{-9} \] \[ y = -\frac{16}{9} \] Therefore, the y-intercept is \( (x, y) = (0, -\frac{16}{9}) \). So, we have: **x-intercept:** \[ (x, y) = (4, 0) \] **y-intercept:** \[ (x, y) = (0, -\frac{16}{9}) \] Here are the steps in summary form: 1. To find the x-intercept, set \( y = 0 \) and solve for \( x \). 2. To find the y-intercept, set \( x = 0 \) and solve for \( y \). These intercepts are crucial for graphing linear equations and understanding their intersections with the axes.
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