Question: What is the equation of the graph below?
A decreasing straight line is shown in the center-left of the page, crossing the y-axis at -3 and the x-axis at about -1.5, so the equation is $y = -2x - 3$. position_hint=top-left
y = -2x - 3
y = 2x - 3
y = -2x + 3
y = 2x + 3
1. **State the problem:** We need to find the equation of a straight line that crosses the y-axis at $-3$ and the x-axis at about $-1.5$.
2. **Recall the slope-intercept form:** The equation of a line is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.
3. **Identify the y-intercept:** From the graph, the line crosses the y-axis at $-3$, so $$b = -3$$.
4. **Find the slope $m$:** The line crosses the x-axis at $x = -1.5$, so at this point, $y=0$. Substitute into the equation:
$$0 = m(-1.5) + (-3)$$
$$0 = -1.5m - 3$$
5. **Solve for $m$:**
$$1.5m = -3$$
$$m = \frac{-3}{1.5} = -2$$
6. **Write the equation:**
$$y = -2x - 3$$
7. **Check the options:** The correct equation is $y = -2x - 3$.
**Final answer:** $y = -2x - 3$