Question #25b4e

1 Answer
Feb 11, 2017

Answer:

#y = (-3*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).

#Gradient = m = (rise) / (run) = (-1 -2) / (3 - (-5)) = -3 / 8.#

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

#y = text(gradient) * x + text(y-intercept) = m * x + c.#

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

#y = - 3/8 * x + c.#

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

#(2) = -3/8 (1) + c = -3/8 + c.#

Rearrange to make c the subject:

#c = 2 + 3/8 = 16/8 + 3/8 = (16+3)/8 = 19 / 8.#

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

#y = -3/8 * x + 19/8.#

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

#y = (-3*x + 19)/8.#