Question

What is an equation of the line that passes through the points left bracket, 0, comma, minus, 8, right bracket
(
0
,
−
8
)
(0,−8) and left bracket, minus, 8, comma, 2, right bracket
(
−
8
,
2
)
(−8,2)?

Answer 1

To find the equation of the line passing through the points (0, -8) and (-8, 2), we first need to find the slope of the line.

The formula to find the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Using the given points, we have:

m = (2 - (-8)) / (-8 - 0)
m = (2 + 8) / (-8)
m = 10 / -8
m = -5/4

Now that we have the slope, we can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)

We can choose either point to substitute into the equation. Let's use (0, -8):

y - (-8) = -5/4(x - 0)

Simplifying this equation, we get:

y + 8 = -5/4x

Then, we can rearrange it to the standard form of a linear equation, which is Ax + By = C:

5/4x + y + 8 = 0

Multiplying both sides by 4 to eliminate the fraction, we have:

5x + 4y + 32 = 0

So, the equation of the line passing through the points (0, -8) and (-8, 2) is 5x + 4y + 32 = 0.