Question

What is the equation of this line?

y= - 3/2x

y= 3/2x

y= - 2/3x

y= 2/3x


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Answer 1

`y=\displaystyle(2)/(3)x`

Explanation:

Hi there!

The given linear equations are organized in slope-intercept form:
`y=mx+b` where m is the slope of the line and b is the y-intercept (the value of y when x=0)

First, we can determine the slope using the following formula:

`m=\displaystyle(y_2-y_1)/(x_2-x_1)` where two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in any two points from the graph that falls on the line (you can see below that I've used (3,2) and (0,0):

`m=\displaystyle(2-0)/(3-0)\\\\m=\displaystyle(2)/(3)`

Therefore, the slope of the line is
`\displaystyle(2)/(3)`. Plug this into
`y=mx+b` as m:

`y=\displaystyle(2)/(3)x+b`

We know that the point (0,0) falls on the line. Because y=0 when x=0, we know that the y-intercept (b) is 0:

`y=\displaystyle(2)/(3)x+0\\\\y=\displaystyle(2)/(3)x`

I hope this helps!