Graph this two-variable equation using the
-and -intercepts and then select your
answer from the choices.

Question

Graph this two-variable equation using the $$ x $$-and $$ y $$-intercepts and then select your answer from the choices. $$ y=2 x+4 $$

UpStudy AI · Accepted Answer

To graph the equation $$ y = 2x + 4 $$ using the $$ x $$- and $$ y $$-intercepts, we will follow these steps:

1. **Find the $$ y $$-intercept**: This occurs when $$ x = 0 $$.
   - Substitute $$ x = 0 $$ into the equation:
   $$
   y = 2(0) + 4 = 4
   $$
   So, the $$ y $$-intercept is $$ (0, 4) $$.

2. **Find the $$ x $$-intercept**: This occurs when $$ y = 0 $$.
   - Set $$ y = 0 $$ and solve for $$ x $$:
   $$
   0 = 2x + 4
   $$
   $$
   2x = -4
   $$
   $$
   x = -2
   $$
   So, the $$ x $$-intercept is $$ (-2, 0) $$.

Now we have the intercepts:
- $$ y $$-intercept: $$ (0, 4) $$
- $$ x $$-intercept: $$ (-2, 0) $$

Next, we can plot these points on a graph and draw a line through them.

Let's proceed to graph the equation.
It seems that I cannot directly plot the graph. However, I can guide you on how to do it:

1. **Draw the axes**: Create a horizontal line for the $$ x $$-axis and a vertical line for the $$ y $$-axis.

2. **Plot the intercepts**:
   - Mark the point $$ (0, 4) $$ on the $$ y $$-axis.
   - Mark the point $$ (-2, 0) $$ on the $$ x $$-axis.

3. **Draw the line**: Connect the two points with a straight line, extending it in both directions.

4. **Label the graph**: You can label the line with the equation $$ y = 2x + 4 $$.

This will give you a visual representation of the equation. If you have specific choices to select from, please provide them, and I can help you determine which one corresponds to the graph of the equation.
To graph the equation $$ y = 2x + 4 $$, plot the $$ y $$-intercept at $$ (0, 4) $$ and the $$ x $$-intercept at $$ (-2, 0) $$. Draw a straight line through these points to represent the equation.

Graph this two-variable equation using the
-and -intercepts and then select your
answer from the choices.

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