Write the equation of the line that passes through the points (3, 6) and (4, 10) using function notation.
f(x) = 4x − 6
f(x) = x + 4
y = x + 4
y = 4x − 6
Its
Y= 4x -6
f(3) = 6
f(4) = 10
[f(4)-f(3) ] / (4-3) = [f(x) -f(4]/(x-4)
[ 10 - 6 ]/(1) = [f(x) - 10] /(x-4)
4 = (f(x)-10)/(x-4)
4 x - 16 = f(x) - 10
f(x) = 4 x - 6
Pls help me
I calculated this on Wolfram Alpha :)
Its an awesome math site
except, using function notation, it is
f(x) = 4x-6
To find the equation of a line passing through two points, you can use the point-slope form of a linear equation, which is given by:
y - y1 = m(x - x1)
Where (x1, y1) represents one of the given points and m is the slope of the line.
First, let's calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (3, 6) and (4, 10), let's substitute the values into the slope formula:
m = (10 - 6) / (4 - 3)
= 4 / 1
= 4
Now that we have the slope, we can choose one of the points. Let's use (3, 6):
y - y1 = m(x - x1)
y - 6 = 4(x - 3)
Expanding the equation:
y - 6 = 4x - 12
Now rearrange the equation to the standard form:
y = 4x - 12 + 6
y = 4x - 6
So, the equation of the line that passes through the points (3, 6) and (4, 10) is y = 4x - 6.
Therefore, the correct answer is: y = 4x - 6.