Find the equation for the line L. Note the x-coordinate of the point Q is 3, y-coordinate of the point P is 17, and the parabola has equation y=x^2+4.
What does the parabola have to do with the line?
Well i think you have use it to find the missing values, like point Q (3,y) and point P (x,17), but i still don't know how to find the equation of the line using these two points.
the line intersects the parabola at those two points.
clearly, Q=(3,13) and P=(√13,17)
Now just use the 2-point form of the line.
To find the equation for the line L, we need to find the slope and the y-intercept of the line.
Let's start by finding the slope. The slope of a line passing through two points, (x1, y1) and (x2, y2), is given by the formula:
m = (y2 - y1) / (x2 - x1)
In this case, we have the coordinates of point P (x1, y1) and the x-coordinate of point Q (x2):
P(?, 17)
Q(3, ?)
To find the y-coordinate of point P, we need to substitute the x-coordinate of point Q (3) into the equation of the parabola:
y = x^2 + 4
17 = (3)^2 + 4
17 = 9 + 4
17 = 13
So, the y-coordinate of point P is 13.
Now we have the coordinates (x1, y1) = (3, 13) and (x2, y2) = (3, 17). We can substitute these values into the slope formula:
m = (17 - 13) / (3 - 3)
m = 4 / 0 (Undefined)
The slope of the line is undefined because the line is vertical.
Since the line is vertical and passes through the point (3, 17), the equation of the line can be written as x = 3.
Therefore, the equation for the line L is x = 3.