Graph the linear function using the slope and -intercept.

Ask by Clark Mcguire. in the United States

Mar 25,2025

Question

Graph the linear function using the slope and $$ y $$-intercept. $$ y=-\frac{5}{3} x+5 $$

UpStudy AI · Accepted Answer

1. Identify the $$ y $$-intercept:
   - The equation is $$ y = -\frac{5}{3}x+5 $$.
   - The $$ y $$-intercept is the point where $$ x=0 $$, so it is $$ (0,5) $$.

2. Determine the slope:
   - The slope is given by $$ -\frac{5}{3} $$.
   - This means for every increase of $$ 3 $$ units in $$ x $$, $$ y $$ decreases by $$ 5 $$ units.

3. Find a second point using the slope:
   - Starting at the $$ y $$-intercept $$ (0,5) $$, if you add $$ 3 $$ to $$ x $$ (i.e., $$ 0+3=3 $$) and subtract $$ 5 $$ from $$ y $$ (i.e., $$ 5-5=0 $$), you get the point $$ (3,0) $$.

4. (Optional) Find a third point to confirm:
   - Alternatively, starting at $$ (0,5) $$, subtract $$ 3 $$ from $$ x $$ (i.e., $$ 0-3=-3 $$) and add $$ 5 $$ to $$ y $$ (i.e., $$ 5+5=10 $$), you obtain the point $$ (-3,10) $$.

5. Graph the function:
   - Plot the $$ y $$-intercept $$ (0,5) $$ on the coordinate plane.
   - Plot the point $$ (3,0) $$ (or $$ (-3,10) $$) using the slope.
   - Draw a straight line through the points $$ (0,5) $$ and $$ (3,0) $$ (and $$ (-3,10) $$ if plotted) to represent the linear function $$ y = -\frac{5}{3}x + 5 $$.
To graph the linear function $$ y = -\frac{5}{3}x + 5 $$: 1. **Find the y-intercept**: When $$ x = 0 $$, $$ y = 5 $$. So, plot the point $$ (0, 5) $$. 2. **Use the slope**: The slope is $$ -\frac{5}{3} $$. This means for every 3 units you move to the right, you move down 5 units. Starting from $$ (0, 5) $$, move 3 units right to $$ x = 3 $$ and 5 units down to $$ y = 0 $$. Plot the point $$ (3, 0) $$. 3. **Draw the line**: Connect the points $$ (0, 5) $$ and $$ (3, 0) $$ with a straight line. This line represents the function $$ y = -\frac{5}{3}x + 5 $$.

Graph the linear function using the slope and -intercept.

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