Determine whether the given points are on the graph of $$ y=2 x+3 $$. Select all points that lie on the graph. (4,6) $$ (-4,-6) $$ $$ (-6,-9) $$ $$ (-1,1) $$

Question

UpStudy AI · Accepted Answer

To determine which points lie on the graph of the equation $$ y = 2x + 3 $$, we'll substitute the $$ x $$-coordinate of each point into the equation and see if the resulting $$ y $$-value matches the given $$ y $$-coordinate.

Let's evaluate each point:

1. **Point (4, 6):**
   $$
   y = 2(4) + 3 = 8 + 3 = 11
   $$
   Given $$ y = 6 $$, which does not equal 11.  
   **Conclusion:** **Not** on the graph.

2. **Point (-4, -6):**
   $$
   y = 2(-4) + 3 = -8 + 3 = -5
   $$
   Given $$ y = -6 $$, which does not equal -5.  
   **Conclusion:** **Not** on the graph.

3. **Point (-6, -9):**
   $$
   y = 2(-6) + 3 = -12 + 3 = -9
   $$
   Given $$ y = -9 $$, which **matches** the calculated value.  
   **Conclusion:** **On** the graph.

4. **Point (-1, 1):**
   $$
   y = 2(-1) + 3 = -2 + 3 = 1
   $$
   Given $$ y = 1 $$, which **matches** the calculated value.  
   **Conclusion:** **On** the graph.

**Summary:**
- **Points on the graph:** $$ (-6, -9) $$ and $$ (-1, 1) $$
- **Points not on the graph:** $$ (4, 6) $$ and $$ (-4, -6) $$

**Answer:** Only the points ( –6, –9 ) and (–1, 1) lie on the graph of $$ y = 2x + 3 $$.
The points that lie on the graph of $$ y = 2x + 3 $$ are (–6, –9) and (–1, 1).

Determine whether the given points are on the graph of \( y=2 x+3 \). Select all points that lie on the graph. (4,6) \( (-4,-6) \) \( (-6,-9) \) \( (-1,1) \)

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions