Find a equation of the line passing through (-1,2) which is parallel to the line with equation 2y=x+4

Thankyou x

remember the point-slope form? Your line has slope 1/2, so the line parallel is

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

So

Y= 1/2x+5/2

To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope.

The given line has an equation of 2y = x + 4. To find the slope of this line, we can rewrite the equation in slope-intercept form (y = mx + b) where m is the slope, and b is the y-intercept:

2y = x + 4
Divide both sides by 2:
y = (1/2)x + 2

So the slope of the given line is 1/2.

Since the line we want to find is parallel to this line, it will also have a slope of 1/2.

We know that the line passes through the point (-1, 2). We can use the point-slope form of a line to find the equation. The point-slope form is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.

Plugging in the values:
y - 2 = (1/2)(x - (-1))
Simplifying:
y - 2 = (1/2)(x + 1)

To get the equation in the desired form (y = mx + b), let's simplify further:
y - 2 = (1/2)x + 1/2
Add 2 to both sides:
y = (1/2)x + 5/2

So the equation of the line passing through (-1, 2) and parallel to the line 2y = x + 4 is y = (1/2)x + 5/2.