Question

Write the equation of a line that is perpendicular to y=7x−2 and passes through the point (14,8).(1 point) y=7x−90 y=10x−17 y=−17x+1067 y=−17x+10

Answer 1

Answer:

$\huge\boxed{y=-\frac{1}{7}x+ 10}$

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:    $\frac{1}{7}$
• Opposite of $\frac{1}{7}$:    $-\frac{1}{7}$

So the slope of this line will be $-\frac{1}{7}$. The y-intercept will change, and we can substitute what we know into the equation $y=mx+b$.

$y = -\frac{1}{7}x+b$

Now, we can substitute a point on the graph (14, 8) into this equation to find b.

• $8 = -\frac{1}{7} \cdot 14 + b$
• $8 = -\frac{14}{7} + b$
• $8 = -2 + b$
• $b = 10$

Now that we know the y-intercept, we can finish off our equation by plugging that in.

$y = -\frac{1}{7}x + 10$

Hope this helped!

Answer 2

Answer:

y=−17x+10

Step-by-step explanation:

shorter version