Question

Find an equation for the line that passes through the points (-5,-1) and (5,4)

Answer 1

y = 0.5x + 1.5

Step-by-step explanation:

The equation of a line that passes through two points (x₁, y₁) and (x₂, y₂) can be calculated as:

`y-y_1=m(x-x_1)`

Where m is the slope and it is equal to:

`m=(y_2-y_1)/(x_2-x_1)`

So, if we replace (x₁, y₁) by (-5, -1) and (x₂, y₂) by (5, 4), we get that the slope is equal to:

`m=(4-(-1))/(5-(-5))=(4+1)/(5+5)=(5)/(10)=0.5`

Then, the equation of the line is:

`\begin{gathered} y-(-1)=0.5(x-(-5)) \\ y+1=0.5(x+5) \end{gathered}`

Finally, if we solve for y, we get:

`\begin{gathered} y+1=0.5x+0.5(5) \\ y+1=0.5x+2.5 \\ y+1-1=0.5x+2.5-1 \\ y=0.5x+1.5 \end{gathered}`

So, the equation of the line is:

y = 0.5x + 1.5