SOLUTION: Find the equation of the line passing through the points {1/5 , 7} , {-2 , 4}. My problem here is that I don't know how to change the given point 1/5 into a whole number.

Question 70206: Find the equation of the line passing through the points {1/5 , 7} , {-2 , 4}.
My problem here is that I don't know how to change the given point 1/5 into a whole number.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Find the equation of the line passing through the points {1/5 , 7} , {-2 , 4}.
.
You don't need to convert the into a "whole number", but maybe it would help you
to change it to its equivalent decimal form which is 0.2 [you can do that conversion
by dividing 5 into 1.0]
If you make that conversion your points are (0.2, 7}, {-2, 4}. Call the first point
(x1, y1) and the second point (x2, y2). By comparing these with the given information
you can see that
x1 = 0.2
x2 = -2
y1 = 7
y2 = 4
The slope of the line joining the two points can be found from the formula:
.

.
Substitute the values for x1, x2, y1, and y2 in the appropriate places of the slope equation
to get

This simplifies to:

and we normally use m to represent the slope. Therefore, you can say m = 1.363636
.
You can now write the equation using:

and substitute for m, y1, and x1 to get:

as the equation.
But if you wanted to stay with the fraction 1/5 as x1, you could write that the
slope m is:

.
You can now work on the value of . Recognize that 2 is the same as
so you can make that substitution to get

Substitute that into the slope equation to get:

Do the division by inverting the denominator and multiplying this inversion times the
numerator:

.
Use the value

for m and substitute it into the equation along with the substitutions
for x1 and y1 to get:
.

.
This is an equivalent form of the answer above that uses decimals in the equation.
Study this carefully. Hopefully it will give you some insight into working with fractions
in writing equations.
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