## Calculus 10th Edition

$y=\frac{7}{2} x-\frac{19}{2}$
Let $(3,1)=(x_{1},y_{1})$ and $(5,8)=(x_{2},y_{2})$ The gradient of a line is given by the equation: gradient$=\frac{y_{2}-,y_{1}}{x_{2}-x_{1}}$ By substituting in the given points, the gradient, $m$, of the line is: $\frac{8-1}{5-3}$ $=\frac{7}{2}$ The equation for a line is given by: $y-y_{1}=m\times(x-x_{1})$ Substituting $m=\frac{7}{2}$ and $(3,1)=(x_{1},y_{1})$ $y-1=\frac{7}{2}( x-3)$ $y-1=\frac{7}{2} x-\frac{21}{2}$ Adding $1$ to both sides, $y=\frac{7}{2} x-\frac{19}{2}$