find an equation of the line passing through the given points. Write the equation in function notation
(4,5) and (2,9)
f(x)=
To find the equation of a line passing through two given points (4,5) and (2,9), we can use the slope-intercept form of the equation, which is written as:
y = mx + b
where m represents the slope of the line, and b represents the y-intercept.
1. First, let's find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4,5) and (2,9), we have:
m = (9 - 5) / (2 - 4)
m = 4 / (-2)
m = -2
2. Next, we can substitute one of the given points and the slope into the equation y = mx + b to solve for the y-intercept (b).
Let's use the point (4,5) from the given points:
5 = -2(4) + b
5 = -8 + b
Adding 8 to both sides, we get:
13 = b
Therefore, the y-intercept (b) is 13.
3. Finally, we can write the equation of the line in function notation:
f(x) = -2x + 13
So, the equation of the line passing through the points (4,5) and (2,9) in function notation is f(x) = -2x + 13.