Mathematics, 06.01.2021 21:20 cheyennebatz3609

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

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Answer from: lizzepacheco

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

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

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

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

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!

Answer from: Quest

answer

see attachment

explanation

the given function is

$y = 2x - 4$

this function has y-intercept at

-4 and a slope of 2.

note that, the graph has a positive slope.

the graph that represents this function is the straight line that moves upward from left to right.

the graph touches the y-axis at -4.

the correct choice is the graph shown in the attachment.

Answer from: Quest

⊂⊃⊂⊃ω $\frac{x}{y}\left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right] \left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right] \\ x^{2} \pi \pi \left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right] \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx x_{123} \left \{ {{y=2} \atop {x=2}} \right. \sqrt[n]{x} x_{123}$