Question

Write a linear equation in the form y = mx + b for the given points

Answer 1

Answer:
`y\text{ = }(-5)/(4)x\text{ - 3}`Explanations:

The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given as:

y - y₁ = m (x - x₁)

Where m is the slope of the line given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

For the given points (-4, 2) and (4, -8)

x₁ = -4, y₁ = 2, x₂ = 4, y₂ = -8

Find the slope, m

m = (-8 -2) / (4 - (-4))

m = -10 / 8

m = -5 / 4

Substituting the values of m, x₁, and y₁ into the equation y - y₁ = m (x - x₁):

`\begin{gathered} y\text{ - 2 = }(-5)/(4)(x\text{ - (-4))} \\ y\text{ - 2 = }(-5)/(4)(x\text{ + 4)} \\ y\text{ - 2 = }(-5)/(4)x\text{ - 5} \end{gathered}`

Simplify the equuation above to the form y = mx + b

`\begin{gathered} y\text{ = }(-5)/(4)x\text{ - 5 + 2} \\ y\text{ = }(-5)/(4)x\text{ - 3} \end{gathered}`