Subjects algebra

Slope Y Intercept A00450

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1. **State the problem:** Determine the slope and y-intercept of the line described by the points given in the graph. 2. **Identify points from the graph:** From the description, the line passes through points such as $(-4,-3)$ and $(-3,-2)$. 3. **Calculate the slope $m$ using the formula:** $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(-4,-3)$ and $(-3,-2)$: $$m = \frac{-2 - (-3)}{-3 - (-4)} = \frac{-2 + 3}{-3 + 4} = \frac{1}{1} = 1$$ 4. **Determine the y-intercept $b$:** The line crosses the y-axis at $y=1$ when $x=0$, so $b=1$. 5. **Write the equation in slope-intercept form:** $$y = mx + b = 1x + 1 = x + 1$$ 6. **Answer:** The slope is $m=1$ and the y-intercept is $1$. Therefore, the correct choice is option a: $m=1$; y-intercept = 1.