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

Mathematics

1 answer:

NikAS [45]2 years ago

3 0

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.

<h2>Perpendicular:</h2>

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, $y = -\frac{2}{7}x+ b$ .

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

<h2>Parallel:</h2>

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 $y = \frac{7}{2}x + b$ .