Answer:
[tex]y = -\frac{1}{2}x + 14[/tex]
Step-by-step explanation:
To find the slope we have to use the slope formula:
[tex]slope = \frac{y2 - y1}{x2 - x1}[/tex]
Let's define the variables:
y2 = 11
y1 = 15
x2 = 6
x1 = -2
Now, plug them in to the equation to find the slope:
[tex]slope = \frac{11 - 15}{6 - (-2)} = -\frac{4}{8} = -\frac{1}{2}[/tex]
The slope is -1/2.
To find the y-intercept we have to use this equation:
[tex]y = -\frac{1}{2}x + b[/tex]
Now, we can plug in one of the points given in the equation to solve for b (the y-intercept). I'm going to use point (6,11).
[tex]11 = -\frac{1}{2}(6) + b\\11 = -\frac{6}{2} + b\\11 = -3 + b\\14 = b[/tex]
14 is the y-intercept.
Since we have both the slope and y-intercept the equation can be written:
[tex]y = -\frac{1}{2}x + 14[/tex]
I hope this helps!!
- Kay :)
