Subjects algebra

Line Point 9Af68A

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1. **State the problem:** We need to find the coordinates of another point on the line $h$ which has a slope of 4 and passes through the point $(20,12)$. 2. **Formula used:** The equation of a line in point-slope form is $$y - y_1 = m(x - x_1)$$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line. 3. **Substitute known values:** Here, $m=4$, $x_1=20$, and $y_1=12$. So, $$y - 12 = 4(x - 20)$$ 4. **Simplify the equation:** $$y - 12 = 4x - 80$$ Add 12 to both sides: $$y = 4x - 80 + 12$$ $$y = 4x - 68$$ 5. **Find another point:** Choose a value for $x$ different from 20, for example $x=21$. 6. **Calculate $y$ for $x=21$:** $$y = 4(21) - 68 = 84 - 68 = 16$$ 7. **Answer:** Another point on the line $h$ is $(21,16)$. This point satisfies the line equation and is different from the given point $(20,12)$.