Question

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

Answer 1

Answer:

y = 2/3x + 4/3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step 1: Find slope m

$m=\frac{4-2}{4-1}$

$m=\frac{2}{3}$

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

Answer 2

Answer:

y = 2/3x+4/3

Step-by-step 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