# Question #25b4e

Feb 11, 2017

$y = \frac{- 3 \cdot x + 19}{8.}$

As the two lines are parallel they have the same gradient, m. The value of m can be found by considering the line joining (3,-1) and (-5,2). Then by using the point (1,2), the value of c is found.

#### Explanation:

As the two lines are parallel they have the same gradient, m. The value of m can be found by considering the line joining (3,-1) and (-5,2).

$G r a \mathrm{di} e n t = m = \frac{r i s e}{r u n} = \frac{- 1 - 2}{3 - \left(- 5\right)} = - \frac{3}{8.}$

Now we can find out the equation of the line passing through (1,2). The equation for a straight line is:

$y = \textrm{\nabla i e n t} \cdot x + \textrm{y - \int e r c e p t} = m \cdot x + c .$

Substitute in the value of m, which has already been found:

$y = - \frac{3}{8} \cdot x + c .$

Now by using the x and y values for the point (1,2):

$\left(2\right) = - \frac{3}{8} \left(1\right) + c = - \frac{3}{8} + c .$

Rearrange to make c the subject:

$c = 2 + \frac{3}{8} = \frac{16}{8} + \frac{3}{8} = \frac{16 + 3}{8} = \frac{19}{8.}$

Finally we can put the value of the y-intercept, to produce the answer:

$y = - \frac{3}{8} \cdot x + \frac{19}{8.}$

or if you like you can combine the terms on the right hand side:

$y = \frac{- 3 \cdot x + 19}{8.}$