Question

Line CD passes through points C(1,3) and D(4,-3). What is the equation of line CD in standard form?

Answer 1

2x + y = 5

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = C (1, 3) and (x₂, y₂ ) = D (4, - 3)

m =
`(-3-3)/(4-1)` =
`(-6)/(3)` = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 3 )

3 = - 2 + c ⇒ c = 3 + 2 = 5

y = - 2x + 5 ← equation in slope- intercept form

Add 2x to both sides

2x + y = 5 ← equation in standard form

Answer 2

(1,3) means x1 = 1 and y1 = 3
(4,-3) means x2 = 4 and y2 = -3

To find slope:
(y2-y1) / (x2-x1)
(-3-3) / (4-1)
-6 / 3
Slope is -2

To find intercept:

y-y1 = m(x - x1)
y - 3 = -2(x - 1)
y - 3 = -2x + 2
y = -2x + 5 :)