Answer:
3. 2x + y = −1
Step-by-step explanation:
To find the equation of the line, we write it first in the slope-intercept form:
[tex]y=mx+q[/tex]
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:
[tex]q=-1[/tex]
Now we have to find the slope, by calculating the rate of change of the line through 2 points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking the two points at (-2,3) and (1,-3), we find:
[tex]m=\frac{-3-3}{1-(-2)}=\frac{-6}{3}=-2[/tex]
So the equation of the line is
[tex]y=-2x-1[/tex]
Now we have to re-arrange it in the standard form, so in the form
[tex]ax+bx=c[/tex]
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:
[tex]y+2x=-1[/tex]
So, option 3).
