Subjects algebra

Line Equation Cd39Bc

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1. **State the problem:** Find the equation of the straight line in the form $y = mx + c$ given it crosses the y-axis at 16 and passes through the point $(2, 40)$. 2. **Recall the formula:** The equation of a straight line is $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept. 3. **Identify known values:** The y-intercept $c = 16$ (since the line crosses the y-axis at 16). 4. **Calculate the slope $m$:** Use the formula for slope between two points $(x_1, y_1)$ and $(x_2, y_2)$: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Here, one point is the y-intercept $(0,16)$ and the other is $(2,40)$. 5. Substitute values: $$m = \frac{40 - 16}{2 - 0} = \frac{24}{2} = 12$$ 6. **Write the equation:** Substitute $m=12$ and $c=16$ into $y = mx + c$: $$y = 12x + 16$$ **Final answer:** $$y = 12x + 16$$