Question

Write the equation 

Answer 1

$a)\ the\ slope-intercept\ form:\ y=mx+b\\--------------------------\\m=\frac{2}{3}\Rightarrow y=\frac{2}{3}x+b\\\\the\ point\ (-3;\ 6)\Rightarrow \frac{2}{3}\times(-3)+b=6\\\\-2+b=6\ \ \ \ \ |add\ 2\ to\ both\ sides\\\\b=8\\\\\boxed{y=\frac{2}{3}x+8}$


$b)\ the\ two-points\ formula:y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\-----------------------------\\the\ points:\ (3;-1);\ (5;\ 7)\\\\y-(-1)=\frac{7-(-1)}{5-3}(x-3)\\\\y+1=\frac{7+1}{2}(x-3)\\\\y+1=\frac{8}{2}(x-3)\\\\y+1=4(x-3)\\\\y+1=4x-12\ \ \ \ \ |subtract\ 1\ from\ both\ sides\\\\\boxed{y=4x-13}$

Answer 2

A. y=2/3x+c
6=((2/3)*-3)+c
6+2.33=c
8.33=c

y=2/3x+8 1/3

B. y=mx+c
m= y2-y1/x2-x1
m= (7--1)/(5-3)
m= 8/2 = 4

7=4x5+c
7-20=c
-13=c

y=4x-13