Answer:
[tex]y = - \frac{1}{6} x + 2[/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
Let's first identify the coordinates of two points on the graph:
(-6, 3) and (6, 1)
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
Slope
[tex] = \frac{3 - 1}{ - 6 - 6} [/tex]
[tex] = \frac{2}{ - 12} [/tex]
[tex] = - \frac{1}{6} [/tex]
Substitute the value of the slope into m in the equation:
[tex]y = - \frac{1}{6} x + c[/tex]
To find the value of c, substitute a pair of coordinates into the equation.
When x= 6, y= 1,
[tex]1 = - \frac{1}{ 6} (6) + c[/tex]
1= -1 +c
c= 1 +1
c= 2
Thus, the equation of the line is y= -⅙x +2.
The y-intercept can also be derived from the graph as we can see that the line passes through the y- axis at (0, 2). This point can also be used to find the slope of the line too.
