Question

Write the equation 

a. a line with slope 2/3 that passes through the point (-3,6)

b. a line that passes through the points (3,-1)and (5,7)

Answer 1

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

Answer 2

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



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