Question

Write an
equation that represents the line.
Use exact numbers.

Answer 1

y = 2/3x+4/3

Explanation:

We have two points ( 1,2) and (4,4)

We can find the slope

m = ( y2-y1)/(x2-x1)

= ( 4-2)/(4-1)

= 2/3

We can use the slope intercept form of the equation of a line

y = mx+b where m is the slope and b is the y intercept

y = 2/3 x+b

Substituting a point into the equation

4 = 2/3(4) + b

4 = 8/3 +b

Subtract 8/3 from each side

12/3 - 8/3 = 8/3 +b-8/3

4/3 = b

y = 2/3x+4/3

Answer 2

y = 2/3x + 4/3

Explanation:

Slope-Intercept Form: y = mx + b

Slope Formula:
`m=(y_2-y_1)/(x_2-x_1)`

Step 1: Find slope m

`m=(4-2)/(4-1)`

`m=(2)/(3)`

y = 2/3x + b

Step 2: Find y-intercept b

2 = 2/3(1) + b

2 = 2/3 + b

b = 4/3

Step 3: Write linear equation

y = 2/3x + 4/3