Question #25b4e

1 Answer
Rory H.
Feb 11, 2017

y=−3⋅x+198.

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=riserun=−1−23−(−5)=−38.

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

y=gradient⋅x+y-intercept=m⋅x+c.

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

y=−38⋅x+c.

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

(2)=−38(1)+c=−38+c.

Rearrange to make c the subject:

c=2+38=168+38=16+38=198.

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

y=−38⋅x+198.

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

y=−3⋅x+198.

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