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

Answer:

$y = \frac{1}{2}x - 2$

Step-by-step explanation:

Given lines,

y = 2x - 5,

y = -x + 1

Subtracting these two equations,

0 = 3x - 6

$\implies 3x = 6$

$\implies x = \frac{6}{3}=2$

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 $y=\frac{1}{2}x+4$ is 1/2.

∵ two parallel lines have same slope.

Hence,

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

$y+1=\frac{1}{2}(x-2)$

$y+1=\frac{1}{2}x - 1$

$y = \frac{1}{2}x - 2$