The question is:
Find an equation of the line. Write the equation using function notation through (4, -4); perpendicular to 7y = x - 14
Answer: The equation of the line is f(x) = -7x + 24
Step-by-step explanation:
We are given a line: 7y = x - 14.
We need to find the slope, and that means we need to rewite the slope in the form y = mx + c. Where m is the slope of the line.
7y = x - 14
Divide both sides by 7
y = (1/7)x - 2
Comparing this with y = mx + c, we can see that the slope, m = 1/7
We want to write an equation that is perpendicular to the equation 7y = x - 14.
The slope of a line perpendicular to a slope m is -1/m.
We have a slope 1/7, a line perpendicular to it has slope -7/1.
Now, we use the point-slope form to find our equation:
[tex]y_2 - y_1 = m(x_2 - x_1)[/tex].
The points given is [tex](4, -4) = (x_1, y_1)[/tex]. Substitute the values into the point-slope form equation.
y - (-4) = -7/1 (x - 4)
y + 4 = -7x + 28
The solution has to be in terms of y, so that we can write it using function notation.
Doing that,
y = -7x + 28 - 4
y = -7x + 24
To write it in function notation, simply put y = f(x)
so f(x) = -7x + 24.
