Question 240679
1. A line passes through (2, –1) and (8, 4).
Find the slope using the slope formula: m = {{{(y2-y1)/(x2-x1)}}}
Assign these as follows
x1=2; y1=-1
x2=8; y2=4
:
m = {{{(4-(-1))/(8-2)}}} = {{{(4+1)/(8-2)}}} = {{{5/6}}} is the slope
:
a. Write an equation for the line in point-slope form.
The point-slope form: y - y1 = m(x - x1)
y - (-1) = {{{5/6}}}(x - 2)
y + 1 = {{{5/6}}}x - {{{5/6}}}*2
y + 1 = {{{5/6}}}x - {{{5/3}}}
y = {{{5/6}}}x - {{{5/3}}} -1
y = {{{5/6}}}x - {{{5/3}}} - {{{3/3}}}
:
y = {{{5/6}}}x - {{{8/3}}}; is the point-slope form
:
; 
b. Rewrite the equation in standard form using integers.
y = {{{5/6}}}x - {{{8/3}}}
Multiply each term by 6 to get rid of the denominators, results
6y = 5x - 2(8)
6y = 5x - 16
-5x + 6y = - 16
They prefer the 1s term to be positive, multiply by -1
5x - 6y = 16
;
:
You can check our equation: 
substitute 8 for x and 4 for y and ensure they = 16