Question

Complete the equation of the line through (-6,5) and (-3,3). use exact numbers y=

Answer 1

Line equation

We know the line equation is expressed by

y = mx + b, where is m is its slope (how inclinated it is) and b is intercept with the y-axis.

Finding m

We find its inclination, its slope, m, by

`\begin{gathered} m=(\Delta y)/(\Delta x) \\ =(y_2-y_1)/(x_2-x_1) \\ \end{gathered}`

Let's say

(x₁, y₁) = (-6, 5)

(x₂, y₂) = (-3, 3)

Then

`\begin{gathered} m=(3-5)/(-3-(-6)) \\ =(-2)/(-3+6)=(-2)/(3) \\ m=-(2)/(3) \end{gathered}`

Then y = -(2/3)x + b,

Finding b

Since b is intercept with the y-axis, we know it intercepts y when x = 0

Using the equation we have found y = -(2/3)x + b, and replacing one point given by the question (x₂, y₂) = (-3, 3)

y = -(2/3)x + b

3 = -(2/3)(-3) + b

3 = -2 + b

3 + 2 = b

Then, b = 5

Therefore,

Answer, y = -(2/3)x + 5,