Question

Write the equation of the line that passes through (2, 5) with a slope of 3 in point-slope form.

Answer 1

y=m(x-x1)+y1

Plug in your given information into the equation

Answer 2

y - y1 = m(x - x1) <--point slope form
using points (2,5) and slope 3
y - 5 = 3(x - 2) <--your answer

Answer 3

Write the equation of the line that passes through (2, 2) and (6, 3) in standard form

Answer 4

Standard form is : Ax + By = C
First we have to find the slope(m)
m = (y2 - y1) / (x2 - x1)
set 1 (2,2).....set 2 (6,3)
m = (3 - 2)/(6 - 2)
m = 1/4
your slope is 1/4
Now we use y = mx + b
using either of the points....I will be using (2,2) and the slope(m) is 1/4
y = mx + b
2 = 1/4(2) + b
2 = 1/2 + b
2 - 1/2 = b
4/2 - 1/2 = b
3/2 = b

y = 1/4x + 3/2 (now we need to turn it into standard form)
to do this, we multiply by common denominator 4
(4)y = (4)1/4x + (4)3/2
4y = x + 6
-x + 4y = 6 (now multiply it by -1 to make x positive)
x - 4y = - 6 <-- this is your equation in standard form