Question

On a coordinate plane, a line goes through (0, negative 4) and (12, 6). A point is at (12, negative 2). What is the equation of the line that is parallel to the given line and passes through the point (12, −2)? y = –Six-fifths x + 10 y = –Six-fifths x + 12 y = –Five-sixths x – 10 y = Five-sixths x – 12

Answer 1

`f(x)=(5)/(6)x-12`

Explanation:

1) So let's first calculate the equation of the line that goes through (0,-4) and (12,6).

`m=(y_(2)-y_(1))/(x_(2)-x_(1))\Rightarrow m=(6-(-4))/(12-0)\Rightarrow m=(10)/(12)\Rightarrow m=(5)/(6)\\\Rightarrow f(x)=(5)/(6)x+b\Rightarrow 6=(5)/(6)*(12)+b\Rightarrow 6=10+b\Rightarrow b=-4\\f(x)=(5)/(6)x-4`

2) As the second line is parallel, they share the same slope value.

so
`m_(1)=m_(2)=(5)/(6)`

Plugging it in x-coordinate a y-coordinate (12,-2)

`f(x)=(5)/(6)x+b\Rightarrow -2=(12)(5)/(6)+b\Rightarrow -2=10+b\Rightarrow b=-12\therefore f(x)=(5)/(6)x-12`

(Check the graph)

Answer 2

y = Five-sixths x – 12

Explanation:

Given that the line goes through points (0,-4) and (12,6) then the slope of the line can be calculated as;

m=rise/run

m=6--4/12-0 = 10/12 = 5/6

A line that is parallel to this line will have a slope of 5/6.

If it passes through point (12,-2) then the equation will be;

Points (12,-2) , (x,y) , m=5/6

y--2/x-12 = 5/6

y+2/x-12 =5/6---------------------perform cross multiplication

6(y+2) = 5(x-12)

6y+12=5x-60--------------collect like terms

6y=5x-60-12

6y=5x-72

y= 5/6x -12