1. **Problem a:** Find the equation of the line with slope $m=2$ and y-intercept $b=5$. The general form of a line is $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept. Substitute $m=2$ and $b=5$: $$y=2x+5$$ 2. **Problem b:** Find the equation of the line with slope $m=-3$ passing through point $(4,7)$. Use the point-slope form: $$y - y_1 = m(x - x_1)$$ where $(x_1,y_1)=(4,7)$ and $m=-3$. Substitute values: $$y - 7 = -3(x - 4)$$ Simplify: $$y - 7 = -3x + 12$$ $$y = -3x + 19$$ 3. **Problem c:** Find the equation of the line passing through points $(4,6)$ and $(12,2)$. First, find the slope: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 6}{12 - 4} = \frac{-4}{8} = -\frac{1}{2}$$ Use point-slope form with point $(4,6)$: $$y - 6 = -\frac{1}{2}(x - 4)$$ Simplify: $$y - 6 = -\frac{1}{2}x + 2$$ $$y = -\frac{1}{2}x + 8$$ **Final answers:** a) $y=2x+5$ b) $y=-3x+19$ c) $y=-\frac{1}{2}x+8$