# What is the equation of the line with slope  m= 3/5  that passes through  (-2,17) ?

Apr 1, 2016

5y - 3x - 91 = 0

#### Explanation:

Writing the equation in the form y = mx + c , where m represents the gradient (slope) and c, the y-intercept.

Equation can be partially written as $y = \frac{3}{5} x + c$

Using (-2,17) to find c , by substituting x = -2 , y = 17 into the equation.

$\Rightarrow 17 = \frac{3}{5} \times \left(- 2\right) + c \Rightarrow c = 17 + \frac{6}{5} = \frac{91}{5}$

equation of line is therefore : $y = \frac{3}{5} x + \frac{91}{5}$

multiplying through by 5 , will eliminate fractions.

hence : 5y = 3x + 91 → 5y - 3x - 91 = 0

All 3 forms are valid equations for the line.