Question

Write an equation for each line in point slope form and then convert it to standard form.
Through (2,3) and (3,5)

Answer 1

first we find the slope by using the slope formula
slope(m) = (y2 - y1) / (x2 - x1)
(2,3)...x1 = 2 and y1 = 3
(3,5)...x2 = 3 and y2 = 5
now we sub
slope(m) = (5 - 3) / (3 - 2)
slope(m) = 2/1 or just 2

point slope form : y - y1 = m(x - x1)
slope(m) = 2
you can use either of your points..(2,3)...x1 = 2 and y1 = 3
now we sub
y - 3 = 2(x - 2) <=== point slope form
y - 3 = 2x - 4
y = 2x - 4 + 3
y = 2x - 1 <===slope intercept form

y = 2x - 1 --- subtract 2x from both sides
-2x + y = -1 -- multiply by -1
2x - y = 1 <=== standard form

or you could have used point slope form with the other point
(3,5)...x1 = 3 and y1 = 5
slope(m) = 2

y - 5 = 2(x - 3) <== point slope form
y - 5 = 2x - 6
y = 2x - 6 + 5
y = 2x - 1 <== slope intercept form

and you can turn it into standard form the same way I did before and you should get the same answer in standard form

your point slope forms for these 2 sets of points may be different, but the standard form will be the same

Answer 2

Got it. Do you mind helping me with one more? @texaschic101