Find the equation of the line parallel to y=2x+6 and passing through (4,5)
To find the equation of a line parallel to a given line and passing through a point, you can use the fact that parallel lines have the same slope.
Given the line y = 2x + 6, we can see that the slope of this line is 2. Therefore, the slope of any line parallel to it will also be 2.
We also know that the line we are looking for passes through the point (4,5). Let's call the equation of the line we are looking for y = mx + b, with m representing the slope and b representing the y-intercept.
Since the line is passing through (4,5), we can plug in these coordinates into the equation:
5 = 2 * 4 + b
5 = 8 + b
To find the value of b, we can subtract 8 from both sides of the equation:
5 - 8 = b
-3 = b
Now that we have the value of b, we can write the equation for the line parallel to y = 2x + 6 and passing through (4,5):
y = 2x - 3
Don't two parallel lines have the same slope?
(4, 5), m = 2.
Y = mx + b.
5 = 2*4 + b,
b = -3.
Eq: Y = 2x - 3.
ever hear of point-slope form?
y-5 = 2(x-4)