What is the equation of the line that passes through the points (4/5,1/5) and (1/2,3/2)?

point-slope form

(standard form)

Let me know if you prefer another form.

Step-by-step explanation:

The slope of a line can be found using provided you are given two points on the line.

We are.

Now you can use that formula.  But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.

 (4/5  ,  1/5)

-( 1/2  ,  3/2)

-----------------

3/10          -13/10

2nd/1st = is our slope.

So the following is point-slope form for a linear equaiton:

Plug in a point .

This gives:

I'm going to distribute:

Now I don't like these fractions so I'm going to multiply both sides by the least common multiply of 2,3, and 6 which is 6:

Add 26x on both sides:

Add 9 on both sides:

This is actually standard form of a line.

It can be simplified though.

Divide both sides by 2:

(standard form)

Step-by-step explanation:

The slope-intercept form of an equation of a line:

m - slope

b - y-intercept

The formula of a slope:

We have two points

Convert fractions to the decimals

(divide the numerator by the denominator) :

Calculate the slope:

Put the value of slope and the coordinates of the first point to the equation of a line:

     multiply both sides by 3

          add 10.4 to both sides

          divide both sides by 3

Finally:

- slope-intercept form

Convert to the standard form (Ax + By = C):

     multiply both sides by 3

         add 13x to both sides

- standard form

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.