Question

Hello! Can someone please help me with this question ? I’ll mark brainly thanks ! :)

Answer 1

Answer:

$\Large\boxed{\text{Perpendicular Equation:} \ y = -\frac{2}{7}x + \frac{22}{7}}$

$\Large\boxed{\text{Parallel Equation:} \ y = \frac{7}{2}x -12}$

Step-by-step explanation:

In order to find the equations that are parallel/perpendicular to the line $y = \frac{7}{2}x - 4$, we need to note a couple things about the relationships between lines and their parallel/perpendicular lines.

• A) If a line is perpendicular to another, the slopes will be opposite reciprocals (for instance $-2$ and $\frac{1}{2}$ - multiplied, they equal -1.)
• B) If a line is parallel to another, they will have the exact same slope.

Perpendicular:

We know that the slope of a perpendicular line will be the the opposite reciprocal of the line we're comparing it to.

Since the slope of our base line is $\frac{7}{2}$, we can find the reciprocal, then the opposite of that.

• Reciprocal of $\frac{7}{2} = \frac{2}{7}$
• Opposite of $\frac{2}{7} = -\frac{2}{7}$

So the slope of this line will be $-\frac{2}{7}$, making our equation $y = -\frac{2}{7}x+ b$

However, y-intercepts will not stay the same. In order to find this, we can substitute the point (4, 2) into our equation to solve for b.

• $2 = -\frac{2}{7} \cdot 4 + b$
• $2 = -\frac{8}{7} + b$
• $b = 2+\frac{8}{7}$
• $b = 2 \frac{8}{7}$
• $b=\frac{22}{7}$

Now we know the y-intercept of this equation is $\frac{22}{7}$. We can now finish off our equation of the line by substituting that in to what we already have,  $y = -\frac{2}{7}x+ b$.

$y = -\frac{2}{7}x+ \frac{22}{7}$

Parallel:

As mentioned earlier, parallel lines will have the exact same slope but not the same y-intercept. Since the slope of our original equation is $\frac{7}{2}$, the slope for this one will also be $\frac{7}{2}$.

So we now know the equation looks something like $y = \frac{7}{2}x + b$.

In order to solve for b, we apply the same logic we did in the perpendicular line and substitute in the point (4, 2) into the equation.

• $2 = \frac{7}{2} \cdot 4 + b$
• $2 = \frac{28}{2}+b$
• $2 = 14+b$
• $b = 2-14$

• $b =-12$

Now that we know the slope and the y-intercept, we can finish off our equation as $y = \frac{7}{2}x -12$.

Hope this helped!