Which statement allows for us to conclude that line m and line n are parallel?

1 answer:

8 0

If two lines are parallel, then their slopes are equal.
If the slopes of two lines are equal, then the lines are parallel.

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Find the equation of the line in slope-intercept form perpendicular to the line y= 3/2x-6 and passing through the point (9,-4)

anygoal [31]

Answer:

y = -(2/3)x + 2

Step-by-step explanation:

Perpendicular lines have slopes that are opposite reciprocals of each other. That means you take the slope, flip the fraction, and change the sign.

Here our given line is y = (3/2)x - 6 so the slope 5/9

The opposite reciprocal of 3/2 is -2/3

We set up the equation

y = -(2/3)x + b

we are given a point (x, y) of (9, -4), so plug that in and solve for b

-4 = -(2/3)(9) + b

-4 = -6 + b

2 = b

So our equation is y = -(2/3)x + 2

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Write the quadratic function with the following transformations: vertical shrink by 3, left 4, down 9.

xz_007 [3.2K]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\$

$\bf \bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see

so, the parent equation could be
y = x² ====> y = A(x + C)² + D

shrink by 3, A = 3
left 4, C = +4
down 9, D = 9

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