Question

What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y equals start fraction one over two end fraction x plus four question mark?

Answer 1

`y = (1)/(2)x - 2`

Explanation:

Given lines,

y = 2x - 5,

y = -x + 1

Subtracting these two equations,

0 = 3x - 6

`\implies 3x = 6`

`\implies x = (6)/(3)=2`

By first equation,

`y=2(2) -5=4-5 = -1`

Thus, point of intersecting would be (2, -1).

Now, the equation of a line is y = mx + c,

Where,

m = slope of the line,

So, the slope of the line
`y=(1)/(2)x+4` is 1/2.

∵ two parallel lines have same slope.

Hence,

Equation of the parallel line passes through (2, -1),

`y+1=(1)/(2)(x-2)`

`y+1=(1)/(2)x - 1`

`y = (1)/(2)x - 2`