Answer:
[tex]\huge\boxed{y=-\frac{1}{7}x+ 10}[/tex]
Step-by-step explanation:
In order to find the equation of this line, we need to note two things.
- A) The slope of two lines that are perpendicular will be opposite reciprocals (that is, multiplying them gets us -1.)
- B) We can substitute a point inside an incomplete equation to try and find a missing value.
So first, let's find the opposite reciprocal of 7 which will be the slope to this equation.
- Reciprocal of 7: [tex]\frac{1}{7}[/tex]
- Opposite of [tex]\frac{1}{7}[/tex]: [tex]-\frac{1}{7}[/tex]
So the slope of this line will be [tex]-\frac{1}{7}[/tex]. The y-intercept will change, and we can substitute what we know into the equation [tex]y=mx+b[/tex].
[tex]y = -\frac{1}{7}x+b[/tex]
Now, we can substitute a point on the graph (14, 8) into this equation to find b.
- [tex]8 = -\frac{1}{7} \cdot 14 + b[/tex]
- [tex]8 = -\frac{14}{7} + b[/tex]
- [tex]8 = -2 + b[/tex]
- [tex]b = 10[/tex]
Now that we know the y-intercept, we can finish off our equation by plugging that in.
[tex]y = -\frac{1}{7}x + 10[/tex]
Hope this helped!
