Answer:
The equation of a line passing through the point (3 , 5) and parallel to Y = 1/2x + 4 is
A) y - 5 = 1/2 (x - 3)
Step-by-step explanation:
Given:
equation of line
[tex]y=\frac{1}{2}x + 4[/tex]
To Find:
The equation of a line passing through the point (3 , 5) and parallel to Y = 1/2x + 4
Solution:
Let A be the point A (x₁ ,y₁ ) ≡ (3 , 5)
on the required equation of a line.
As the required line is parallel slope of the line are equal.
On comparing the [tex]y=\frac{1}{2}x + 4[/tex]
equation with
[tex]y=mx +c[/tex]
slope =m =[tex]\frac{1}{2}[/tex]
∴ slope of the required line is also m =[tex]\frac{1}{2}[/tex]
as lines parallel.
We know that equation of line having slope m and passing through point (x₁ ,y₁ )is given by
[tex](y-y_{1})= m(x-x_{1})[/tex]
so on substituting the above values i.e m=[tex]\frac{1}{2}[/tex] and A (x₁ ,y₁ ) ≡ (3 , 5)
we get
[tex]y-5=\frac{1}{2}(x-3)[/tex]
∴ [tex]y-5=\frac{1}{2}(x-3)[/tex] as per required
