Subjects algebra

Line Sketch B07Aa2

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1. **State the problem:** We are asked to sketch the line given by the equation $$y=\frac{1}{2}x - 1$$. 2. **Recall the slope-intercept form:** The equation of a line in slope-intercept form is $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, the slope $m=\frac{1}{2}$ and the y-intercept $b=-1$. 4. **Plot the y-intercept:** The line crosses the y-axis at $(0,-1)$. 5. **Use the slope to find another point:** The slope $\frac{1}{2}$ means rise over run is $1$ over $2$. From $(0,-1)$, move up 1 unit and right 2 units to reach the point $(2,0)$. 6. **Draw the line:** Connect the points $(0,-1)$ and $(2,0)$ with a straight line extending in both directions. 7. **Summary:** The line passes through $(0,-1)$ and $(2,0)$ with slope $\frac{1}{2}$. **Final answer:** The graph of $$y=\frac{1}{2}x - 1$$ is a line with slope $\frac{1}{2}$ and y-intercept $-1$ passing through points $(0,-1)$ and $(2,0)$.