Graph the line that passes through 24. $$ (-3,-2) ; m=2 $$

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UpStudy AI · Accepted Answer

To graph the line that passes through the point $$(-3, -2)$$ with a slope $$m = 2$$, we can use the point-slope form of the equation of a line, which is given by:

$$
y - y_1 = m(x - x_1)
$$

where $$(x_1, y_1)$$ is a point on the line and $$m$$ is the slope.

### Step 1: Substitute the known values
Here, $$(x_1, y_1) = (-3, -2)$$ and $$m = 2$$. Substituting these values into the equation gives:

$$
y - (-2) = 2(x - (-3))
$$

This simplifies to:

$$
y + 2 = 2(x + 3)
$$

### Step 2: Simplify the equation
Now, we can simplify this equation:

$$
y + 2 = 2x + 6
$$

Subtracting 2 from both sides:

$$
y = 2x + 4
$$

### Step 3: Graph the line
To graph the line $$y = 2x + 4$$:

1. **Identify the y-intercept**: The y-intercept is $$4$$ (where the line crosses the y-axis).
2. **Use the slope**: The slope $$2$$ means that for every 1 unit you move to the right (positive x-direction), you move up 2 units (positive y-direction).

### Step 4: Plot points
- Start at the y-intercept $$(0, 4)$$.
- From there, move right 1 unit to $$x = 1$$ and up 2 units to $$y = 6$$, giving the point $$(1, 6)$$.
- You can also go left from the y-intercept: move left 1 unit to $$x = -1$$ and down 2 units to $$y = 2$$, giving the point $$(-1, 2)$$.

### Final Graph
You can now draw a straight line through the points $$(-3, -2)$$, $$(0, 4)$$, and $$(1, 6)$$ to represent the line $$y = 2x + 4$$.

If you have graphing software or graph paper, you can plot these points and draw the line accordingly.
To graph the line passing through $$(-3, -2)$$ with a slope of 2, use the equation $$y = 2x + 4$$. Plot the y-intercept at $$(0, 4)$$ and another point like $$(1, 6)$$. Draw a straight line through these points to represent the line.

Graph the line that passes through
24.

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