Questions: Solve graphically. x+y = 12 5x+y = 0

Transcript text: Solve graphically. \[ \begin{aligned} x+y & =12 \\ 5 x+y & =0 \end{aligned} \]

Solution

Solution Steps

Step 1: Rewrite the equations in slope-intercept form.

The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

$x + y = 12 \Rightarrow y = -x + 12$ $5x + y = 0 \Rightarrow y = -5x$

Step 2: Identify the slope and y-intercept of each equation.

For $y = -x + 12$, the slope is $-1$ and the y-intercept is $12$. For $y = -5x$, the slope is $-5$ and the y-intercept is $0$.

Step 3: Plot the y-intercepts.

Plot the point $(0, 12)$ for the first equation. Plot the point $(0, 0)$ for the second equation.

Step 4: Use the slope to find another point on each line.

For the first equation ($y = -x + 12$), the slope is $-1$. From the y-intercept $(0, 12)$, move down 1 unit and right 1 unit to find another point $(1, 11)$. For the second equation ($y = -5x$), the slope is $-5$. From the y-intercept $(0, 0)$, move down 5 units and right 1 unit to find another point $(1, -5)$.

Step 5: Draw the lines.

Draw a line through the points $(0, 12)$ and $(1, 11)$. Draw a line through the points $(0, 0)$ and $(1, -5)$.

Step 6: Identify the point of intersection.

The lines intersect at the point $(-3, 15)$.