# What is the equation in point-slope form and slope intercept form of the line given slope 3⁄5 that passes through the point (10, −2)?

Jun 1, 2015

point-slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right) m = s l o p e \mathmr{and} \left({x}_{1} , {y}_{1}\right)$ is the point
slope-intercept form: $y = m x + c$

1)$y - \left(- 2\right) = \frac{3}{5} \left(x - 10\right) \implies y + 2 = \frac{3}{5} \left(x\right) - 6$

$5 y - 3 x - 40 = 0$

2)$y = m x + c$
$- 2 = \frac{3}{5} \left(10\right) + c \implies - 2 = 6 + c \implies c = - 8$(which can be observed from the previous equation also)

$y = \frac{3}{5} \left(x\right) - 8 \implies 5 y - 3 x - 40 = 0$