Answer:
y = (1/2)x + (yP - (1/2)xP)
Explanation:
To find a parallel line to line jk that passes through point P, we need to use the fact that parallel lines have the same slope.
First, let's find the slope of line jk. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-4, 5) and (2, 8), we have:
m = (8 - 5) / (2 - (-4)) = 3/6 = 1/2
So the slope of line jk is 1/2.
Now, let's use the point P and the slope of line jk to find the equation of the parallel line that passes through point P. We can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Let's assume that point P has coordinates (xP, yP). Then the equation of the parallel line passing through P is:
y - yP = (1/2)(x - xP)
Simplifying this equation, we get:
y = (1/2)x + (yP - (1/2)xP)
So the equation of the parallel line passing through point P is:
y = (1/2)x + C
where C = yP - (1/2)xP is a constant. This equation represents all possible parallel lines passing through point P.
Hope this helps!