Answer:
y = 3.33x - 18
Step-by-step explanation:
In order for a line to be perpendicular to another, it must have a slope with the negative reciprocal
- Here in the equation y = -0.3z + 6 has a slope of -0.3 (can also be written as [tex]-\frac{3}{10}[/tex])
- A line that is perpendicular to this line will need to have a slope of 3.33 repeating (or [tex]\frac{10}{3}[/tex])
- I will using fractions for simplicity and convert to decimals afterwards
Since we have our slope and the two points, we can plug them into y = mx + b to solve for b and write our new equation of a line
- Substituting in the values that we have we get: [tex]-8=\frac{10}{3}(3)+b[/tex]
- Simplifying we get -8 = 10 + b, making b = -18
Now that we have our slope and our y-intercept we can plug them into the same formula used before to find our perpendicular line:
- [tex]y= \frac{10}{3}x-18[/tex] which can also be written as y = 3.33x - 18
