Subjects algebra

Find Another Point 6Fe9Aa

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Find Another Point 6Fe9Aa


1. **State the problem:** Find another point on the line with slope $\frac{7}{5}$ passing through the point $(-3,-2)$. 2. **Recall the slope formula:** The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Given:** $m = \frac{7}{5}$, $(x_1,y_1) = (-3,-2)$, find $(x_2,y_2)$. 4. **Choose a convenient $x_2$:** To find another point, pick $x_2 = 2$ (any value different from $x_1$). 5. **Use the slope formula to find $y_2$:** $$\frac{y_2 - (-2)}{2 - (-3)} = \frac{7}{5}$$ $$\frac{y_2 + 2}{5} = \frac{7}{5}$$ 6. **Multiply both sides by 5:** $$y_2 + 2 = 7$$ 7. **Solve for $y_2$:** $$y_2 = 7 - 2 = 5$$ 8. **Conclusion:** Another point on the line is $(2,5)$.