a. Rewrite the given equation in slope-intercept form by
solving for .
b. Give the slope and -intercept.
c. Use the slope and -intercept to graph the linear
function.

Ask by Bowen Li. in the United States

Mar 25,2025

Question

a. Rewrite the given equation in slope-intercept form by
solving for .
b. Give the slope and -intercept.
c. Use the slope and -intercept to graph the linear
function.

Ask by Bowen Li. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

1. **Rewrite in Slope-Intercept Form:**  
   Starting with  
   $$
   3x + y = 8,
   $$  
   subtract $$ 3x $$ from both sides to solve for $$ y $$:
   $$
   y = 8 - 3x.
   $$  
   This can be rewritten as  
   $$
   y = -3x + 8.
   $$

2. **Identify Slope and $$ y $$-intercept:**  
   In the slope-intercept form $$ y = mx + b $$, the slope $$ m $$ is $$-3$$ and the $$ y $$-intercept $$ b $$ is $$ 8 $$.  
   - Slope: $$ m = -3 $$  
   - $$ y $$-intercept: $$ (0, 8) $$

3. **Graph the Linear Function:**  
   - First, plot the $$ y $$-intercept at $$ (0, 8) $$.  
   - Next, use the slope $$-3$$ which tells you that for every 1 unit increase in $$ x $$, $$ y $$ decreases by 3. From the point $$ (0, 8) $$, moving 1 unit to the right gives $$ x = 1 $$ and $$ y = 8 - 3 = 5 $$, so plot the point $$ (1, 5) $$.  
   - Similarly, you can use the slope in the opposite direction: moving 1 unit to the left (i.e., $$ x = -1 $$), $$ y = 8 + 3 = 11 $$, and plot the point $$ (-1, 11) $$.  
   - Draw a straight line through these points to complete the graph.
a. Rewrite the equation in slope-intercept form: $$ y = -3x + 8 $$ b. Slope ($$ m $$) is $$-3$$ and $$ y $$-intercept ($$ b $$) is $$ 8 $$. c. To graph the function: - Plot the $$ y $$-intercept at $$ (0, 8) $$. - Use the slope $$-3$$ to find another point, such as $$ (1, 5) $$. - Draw a straight line through these points.

a. Rewrite the given equation in slope-intercept form by
solving for .
b. Give the slope and -intercept.
c. Use the slope and -intercept to graph the linear
function.

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a. Rewrite the given equation in slope-intercept form by
solving for .
b. Give the slope and -intercept.
c. Use the slope and -intercept to graph the linear
function.