Certainly! Let's explore the graph of the linear equation: \[ y + x = 14 \] ### Step 1: Rewrite the Equation in Slope-Intercept Form First, it's helpful to rewrite the equation in the slope-intercept form, which is: \[ y = mx + b \] Where: - $$ m $$ is the slope. - $$ b $$ is the y-intercept. Starting with: \[ y + x = 14 \] Subtract $$ x $$ from both sides to solve for $$ y $$: \[ y = -x + 14 \] Now, the equation is in slope-intercept form where: - **Slope ($$ m $$)** = -1 - **Y-intercept ($$ b $$)** = 14 ### Step 2: Determine Key Points for the Graph To plot the graph, we'll find two points by choosing values for $$ x $$ and solving for $$ y $$. 1. **Y-Intercept Point:** - When $$ x = 0 $$: \[ y = -0 + 14 = 14 \] - So, one point is $$ (0, 14) $$. 2. **X-Intercept Point:** - To find the x-intercept, set $$ y = 0 $$: \[ 0 = -x + 14 \\ x = 14 \] - So, another point is $$ (14, 0) $$. 3. **Additional Point (optional):** - Choose another value for $$ x $$, say $$ x = 7 $$: \[ y = -7 + 14 = 7 \] - This gives the point $$ (7, 7) $$. ### Step 3: Plot the Points and Draw the Line Here's a simple representation of the graph using these points: ``` Y | 14 |* | 12 | | 10 | | 8 | | 6 | | 4 | | 2 | | 0 *--------------------------- X 0 14 ``` - **Point $$ (0, 14) $$** is the y-intercept. - **Point $$ (14, 0) $$** is the x-intercept. - **Point $$ (7, 7) $$** lies on the line between them. **Connecting these points** with a straight line will give you the graph of the equation $$ y + x = 14 $$. ### Step 4: Understanding the Graph - **Slope ($$ m = -1 $$)**: This indicates that for every unit increase in $$ x $$, $$ y $$ decreases by 1 unit. The line slopes downward from left to right. - **Y-Intercept ($$ b = 14 $$)**: The line crosses the y-axis at $$ y = 14 $$. ### Visual Graph While I can't provide a graphical image directly, here's a more detailed ASCII representation to help visualize: ``` Y | 14 | * | 12 | | 10 | | 8 | | 6 | | 4 | | 2 | | 0 *------------------------------- X 0 2 4 6 8 10 12 14 ``` - The asterisk (*) at $$ (0, 14) $$ and $$ (14, 0) $$ signifies the intercepts. - You can draw a straight line connecting these points to represent the equation. ### Summary The graph of $$ y + x = 14 $$ is a straight line with a slope of -1 and a y-intercept at (0, 14). It crosses the x-axis at (14, 0). By plotting these points and drawing a line through them, you can visualize the relationship between $$ x $$ and $$ y $$ as described by the equation. If you have access to graphing tools like Desmos, GeoGebra, or even graph paper, I encourage you to plot these points for a clearer visual representation! The graph of $$ y + x = 14 $$ is a straight line with a slope of -1 and crosses the y-axis at (0, 14) and the x-axis at (14, 0).

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graph $ y+x=14 $

Ask by Coleman Hamilton. in the United States

Jan 23,2025

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The graph of $ y + x = 14 $ is a straight line with a slope of -1 and crosses the y-axis at (0, 14) and the x-axis at (14, 0).

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To graph the equation $ y + x = 14 $, first, you can rearrange it into slope-intercept form (y = mx + b), resulting in $ y = -x + 14 $. This tells you the y-intercept is 14, which is where the line crosses the y-axis. Start by plotting the point (0, 14). Then, for a second point, you can let x be 14 (resulting in (14, 0)), and connect these points with a straight line. You'll find that this line has a negative slope, meaning it goes downhill from left to right. It's always a good idea to include a couple more points to ensure accuracy in your graphing. Happy plotting!

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