Mathematics, 12.07.2019 05:00 dariagodoy8

Write an equation for each translation of y=|x|. 13 units down

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Answer from: aiffland113

The answer is y = |x| - 13

Answer from: dillpickle124617

y = |x| - 13.

Step-by-step explanation:

We know that,

Translation is a transformation that shifts the figure in any direction by some scale factor.

The general form for horizontal translation of a function f(x) is f(x \pm k) and vertical translation is f(x) \pm k, where k is any constant.

We are given y = |x| and are required to translate it 13 units down.

Which means that we are asked to translate the function y = |x| vertically 13 units down.

So, comparing with the general form, we get that the equation for translating y = |x| 13 units down is y = |x| - 13.

It can also be seen below that the graph of y = |x| -13 translates the function 13 units down.

Write an equation for each translation of y=|x|. 13 units down

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

step-by-step explanation:

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