Question

Which of the following are equations for the line shown below? Check all thatapply.5(-5, -2)(3,-4)

Answer 1

To solve this problem, we need to apply the formula for the equation of a straight line.

One of the forms of this formula, which is appropriate for this problem, is as follows:

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Where (x1 , y1) and (x2 , y2), are the coordinates of any two points that lie on the line.

In this case, the coordinates are: ( -5,-2), and (3, -4)

Now:

`\frac{y-(-2)_{}}{x-(-5)_{}}=\frac{-4_{}-(-2)_{}}{3_{}-(-5)_{}}`
`\frac{y+2_{}}{x+5_{}}=\frac{-4_{}+2_{}}{3_{}+5_{}}`
`\frac{y+2_{}}{x+5_{}}=\frac{-2_{}}{8_{}}`

`\frac{y+2_{}}{x+5_{}}=\frac{-1_{}}{4_{}}`
`\frac{y+2_{}}{x+5_{}}=-0.25`
`\begin{gathered} y+2_{}=-0.25(x+5)\text{ (OPTION C is correct)} \\ y+2_{}=-0.25x-1.25\text{ Option D is also correct} \\ y=-0.25x-3,25\text{ } \end{gathered}`