Question

What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 7, and is also parallel to the line y= 1/2x+4?

y= -1/2x-3
y= 1/2x+1
y =-1/2x+4
y = 2x − 1

Answer 1

First, we will need to find the point of intersections between the first two lines. To do this, we set the equations equal to each other and solve for
`x`:

`2x - 5 = -x + 7`

`3x - 5 = 7`

`x = 4`

Now, we can insert this value for
`x` back into one of our original equations to find the y-value of the coordinate:

`2(4) - 5 = 3`

So, the point of intersection of the lines is (4, 3). Now, we need to find the equation of the other line. Since, we know that this unknown line is parallel to the line
`y = (1)/(2)x + 4`, we can say that our unkown line has a slope of
`(1)/(2)`. Since we have a point on our unknown line and the value of its slope, we can use the point-slope formula to find the equation of our line.

Remember that the point-slope formula is
`(y - y_1) = m(x - x_1)`, where
`m` is the slope of the line,
`x_1` is the x-coordinate of our point, and
`y_1` is the y-coordinate of our point:

`(y - 3) = (1)/(2)(x - 4)`

`y = (1)/(2)x - 2 + 3`

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

Our answer is the second choice, or
`\boxed{y = (1)/(2)x + 1}`.