Subjects algebra

Line Equation Befd3A

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Question: What is the equation of the straight line shown below? Give your answer in the form $y = mx + c$ Graph: a straight orange line rises from bottom-left to top-right, crossing the y-axis at $(0, 12)$ and the x-axis at $(-1, 0)$; position_hint=center.
1. **State the problem:** Find the equation of the straight line in the form $y = mx + c$ given it crosses the y-axis at $(0, 12)$ and the x-axis at $(-1, 0)$. 2. **Recall the formula:** The equation of a line is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 3. **Identify the y-intercept:** From the point $(0, 12)$, the y-intercept $c = 12$. 4. **Calculate the slope $m$:** The slope is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(-1, 0)$ and $(0, 12)$: $$m = \frac{12 - 0}{0 - (-1)} = \frac{12}{1} = 12$$ 5. **Write the equation:** Substitute $m = 12$ and $c = 12$ into $y = mx + c$: $$y = 12x + 12$$ 6. **Final answer:** The equation of the line is $y = 12x + 12$.