1. The problem is to find the equation of the line passing through the points $A(2,3)$ and $B(4,7)$. 2. The formula for the slope $m$ of a line through two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m=\frac{y_2-y_1}{x_2-x_1}$$ 3. Substitute the coordinates of points $A$ and $B$: $$m=\frac{7-3}{4-2}=\frac{4}{2}$$ 4. Simplify the fraction: $$m=\frac{\cancel{4}}{\cancel{2}}=2$$ 5. Use the point-slope form of the line equation: $$y-y_1=m(x-x_1)$$ 6. Substitute $m=2$ and point $A(2,3)$: $$y-3=2(x-2)$$ 7. Expand the right side: $$y-3=2x-4$$ 8. Add 3 to both sides: $$y=2x-4+3$$ 9. Simplify: $$y=2x-1$$ The equation of the line passing through points $A(2,3)$ and $B(4,7)$ is $$y=2x-1$$.