find an equation of the line containing the given pair of points. Use function notation to write the equation.
(5/7,10/14) and (-1/7,13/14)
f(x)
The slope is (13/14 - 10/14)/(-1/7 - 5/7)
= -1/4
so the equation is y = (-1/4)x + b
plug in the first point
10/14 = (-1/4)(5/7) + b
times 28
20 = -5 + 28b
b = 25/28
y = (-1/4)x + 25/28
This is not a good question. If the purpose of the question is to see if you can find the equation of a line given two points, then using "simple" numbers would test that.
This is like having a 100 m butterfly race but insisting that all swimmers wear boots.
To find the equation of the line passing through two points, we can use the point-slope form of the linear equation. The formula is:
y - y1 = m(x - x1),
where m is the slope of the line and (x1, y1) is one of the points on the line.
Let's begin by finding the slope of the line using the given points:
Slope (m) = (y2 - y1) / (x2 - x1),
where (x1, y1) = (5/7, 10/14) and (x2, y2) = (-1/7, 13/14).
Substituting the values:
m = (13/14 - 10/14) / (-1/7 - 5/7)
= (3/14) / (-6/7)
= (3/14) * (-7/6)
= -3/8.
Now that we have the slope, we can choose one of the given points and use the point-slope form to find the equation of the line. Let's use the first point (5/7, 10/14):
y - y1 = m(x - x1)
y - 10/14 = -3/8(x - 5/7).
To simplify this equation, multiply through by the least common denominator (LCD) of 14:
14(y - 10/14) = -3/8(14)(x - 5/7)
14y - 10 = -21/8(x - 5/7).
Next, simplify further by distributing the terms:
14y - 10 = -21/8x + 105/56.
To eliminate fractions, multiply through by the denominator 8:
8(14y - 10) = 8(-21/8x + 105/56)
112y - 80 = -21x + 15.
Finally, rearrange the equation into the general form:
21x + 112y = 95.
Therefore, the equation of the line passing through the points (5/7, 10/14) and (-1/7, 13/14) is:
21x + 112y = 95.
We can write this equation using function notation as:
f(x) = (-21/112)x + (95/112).