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lara31 [8.8K]
3 years ago
8

What happens to a line when the y-intercept is changed? Check all that apply. A. As the y-intercept increases, the graph of the

line shifts up. B. as the y-intercept decreases, the graph of the line shifts left. C. As the y-intercept increases, the graph of the line gets steeper. D. As the y-intercept decreases, the graph of the line shifts down. E. as the y-intercept increases, the graph of the line shifts right.
Mathematics
2 answers:
olga nikolaevna [1]3 years ago
5 0
<span>Answer: two options apply: A and D.
</span>
<span /><span /><span>A. As the y-intercept increases, the graph of the line shifts up.

D. As the y-intercept decreases, the graph of the line shifts down.
</span><span />

<span>Justification:


</span><span>1) Take the slope-intercept equation of the line: y = f(x) = mx + b</span>
<span /><span>
</span><span>2) The y-intercept is b
</span>
<span /><span /><span>
3) When b is increased, f(x) will increases too, that is f(x) will be higher or its graph will be shifted up, which is what the option A. states.
</span><span />

<span>4) When b is decreased, f(x) will decreases too, that is f(x) will be lower or its graph will be shifted dOwn, which is what the option D states.
</span><span />

<span>5) Regarding the options B and E, which deal with motions in the horizontal direction (left or righT), nothing can be said, as the effect of a change in the y -intercept on the horizontal direction will depend on the slope.
</span><span />

<span>6) Regarding the option C, a change in the y-intercept does not change the slope (the steep of the line).
</span><span />

USPshnik [31]3 years ago
3 0

Answer:

A. As the y-intercept increases, the graph of the line shifts up.

D. As the y-intercept decreases, the graph of the line shifts down.

Step-by-step explanation:

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John held a garage sale. He priced all the items at a dime or a quarter, his sales totaled less than $5, the solution is shaded region in quadrant I.

<h3>What is a slope?</h3>

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He priced all items at a dime or a quarter. His sales totaled less than $5

Since dime =$ 0.10=$0.10 and the quarter =$0.25=$0.25

Let x=x= the number of the items sold for a dime

Let y=y= the number of the items sold for a quarter

0.10x+0.25y<5

0.10x+0.25y<5

Inequality in the slope-intercept form

0.10x+0.25y Subtract 0.10x from both sides

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y= -\frac{2}{5}x+20\\

The slope is, -\frac{2}{5} and the y- intercept is 20

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Test point (0,0)(0,0)

Substituting the values 0 for x and 0 for y,

y < -\frac{2}{5}x+20\\\\0 < -\frac{2}{5}(0)+20\\\\0 < +20

Since inequality is true

So, (0,0)(0,0) is solution of the inequality

Shade region containing (0,0)(0,0).

The graph below shows all possible solutions

Since boundary line is dashed and the number of items is always positive

The solution is shaded region in quadrant I

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