Question

What is the equation of the following line? Be sure to scroll down first to seeall answer options.10(7,2)+- 10(0, 0)10-10 -O A. y=-7x

Answer 1

Step 1. Let's remember the general equation for a line, also known as the slope-intercept equation:

`y=mx+b`

Where m represents the slope of the line and b represents the y-intercept of the line. By finding m and b and substituting them into the general equation, we will have found the equation of the line.

Step 2. Now that we know the general equation, let's find b.

As we said in step 1, b represents the y-intercept of the line, which is the point where the line crosses the y-axis.

As we can see in the following image:

The line crosses the y-axis at 0. So the y-intercept is 0:

`b=0`

Substituting this in the general line equation from step 1:

`\begin{gathered} y=mx+0 \\ y=mx \end{gathered}`

Step 3. The last thing we need is to find "m" --> The slope of the line.

For this, we take two points through which the line passes, those two points are already marked in the given graph:

`(0,0)\text{ and (}7,2\text{)}`

For reference, we will label the x-and y-coordinates of these points as follows:

`\begin{gathered} x_1=0 \\ y_1=0 \\ x_2=7 \\ y_2=2 \end{gathered}`

And now, we have to use the slope formula:

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

And substitute the values we labeled previously:

`m=(2-0)/(7-0)`

Solving the operations:

`m=(2)/(7)`

Step 4. Remember that we needed m to substitute it into the general equation, so now that we have it, we can find the equation of the line:

`y=(2)/(7)x`

Answer: C