Question

What is the standard form equation of the line shown below? Graph of a line going through negative 2, 3 and 1, negative 3

1. y + 3 = −2(x − 1)
2. y = −2x − 1
3. 2x + y = −1
4. −2x − y = 1

Answer 1

3. 2x + y = −1

Explanation:

To find the equation of the line, we write it first in the slope-intercept form:

`y=mx+q`

where

m is the slope

q is the y-intercept

From the graph, we see that the line crosses the y-axis at y = -1, so the y-intercept is -1:

`q=-1`

Now we have to find the slope, by calculating the rate of change of the line through 2 points:

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

Taking the two points at (-2,3) and (1,-3), we find:

`m=(-3-3)/(1-(-2))=(-6)/(3)=-2`

So the equation of the line is

`y=-2x-1`

Now we have to re-arrange it in the standard form, so in the form

`ax+bx=c`

where a, b and c are integer numbers.

To do that, we simply add +2x on both sides of the equation of the line in the slope-intercept form, and we get:

`y+2x=-1`

So, option 3).