Question

What is the linear equation of (0.5,10) and -4.5,-10​

Answer 1

The linear equation containing the points (0.5, 10) and (-4.5, -10) will be:

• 
  `y=4x+8`

Please check the attached graph also.

Explanation:

Given the points

• (0.5, 10)

• (-4.5, -10)

Finding the slope between (0.5, 10) and (-4.5, -10)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(0.5,\:10\right),\:\left(x_2,\:y_2\right)=\left(-4.5,\:-10\right)`

`m=(-10-10)/(-4.5-0.5)`

Refine

`m=4`

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where

• m is the slope of the line

• (x₁, y₁) is the point

substituting the values m = 4 and the point (0.5, 10) in the point-slope form

`y-y_1=m\left(x-x_1\right)`

`y - 10 = 4(x-0.5)`

Add 10 to both sides

`y-10+10=4\left(x-0.5\right)+10`

Simplify

`y=4x+8`

Therefore, the linear equation containing the points (0.5, 10) and (-4.5, -10) will be:

• 
  `y=4x+8`

Please check the attached graph also.