Question

Find the equation of the line containing the following two points: (0,-10) and (-5,0).

Answer 1

`\boxed{y=-2x-10}`

Step-by-step explanation:

Step 1. The two points we have are:

`\begin{gathered} (0,-10) \\ \text{and} \\ (-5,0) \end{gathered}`

We will label these points as (x1,y1) and (x2,y2):

`\begin{gathered} x_1=0 \\ y_1=-10 \\ x_1=-5 \\ y_1=0 \end{gathered}`

Step 2. The second step is to find the slope ''m'' of the line, which is defined as follows:

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

Substituting the known values from step 1:

`m=(0-(-10))/(-5-0)`

Solving the operations:

`\begin{gathered} m=(10)/(-5) \\ \downarrow \\ m=-2 \end{gathered}`

Step 3. Next, we need to find the y-intercept of the line.

The y-intercept is the value of y when the value of x is 0. In this case, we are already given this information in the first point:

(0, -10)

This indicates that the y-value is -10 when the x-value is 0.

The y-intercept is -10, this will be labeled as ''b'':

`b=-10`

Step 4. Use the values for ''m'' and ''b'' in the general slope-intercept equation:

`y=mx+b`

Substituting m and b:

`\begin{gathered} \\ \boxed{y=-2x-10} \end{gathered}`

Answer:

`\boxed{y=-2x-10}`