Describe what happens to the graph of y=3x + 4 when the slope is changed 1/3 one over three

Mathematics

1 answer:

kumpel [21]3 years ago

5 0

Answer:

see the explanation

The graph in the attached figure

Step-by-step explanation:

we have

$y=3x+4$

This is a linear equation (the graph is a line)

The y-intercept is the point (0,4) ---> value of y when the value of x is equal to zero)

The x-intercept is the point (-4/3,0) ---> value of x when the value of y is equal to zero)

The slope is m=3

If the slope is changed to m=1/3

we have

$y=(1/3)x+4$

This is a linear equation too (the graph is a line)

The y-intercept is the point (0,4) ---> is the same

The x-intercept is the point (-12,0) ---> the x-intercept is different

The slope is m=1/3

The second line becomes a lot less steep

Remember that the slope is the ratio between the rise and the run

In the first line the ratio rise/run is 4/1

In the second line the ratio rise/run is 1/3

see the attached figure to better understand the problem

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What is value of x?<br> Enter your answer in the box.

marin [14]

Answer:

$x \ = \ 10$

Step-by-step explanation:

Let point $D$ be the point where the straight line drawn from point $A$ meets the straight line $BC$ , it is evident that $\triangle ABD$ and $\triangle ACD$ is similar given that both triangles share the same angle, $\angle BAD \ = \ \angle DAC$ . Hence, the ratio of the sides of each triangle is the same. Specifically,

$\displaystyle{\frac{x+4}{8} \ = \ \frac{2x+1}{12}}$ .

Performing cross multiplication yields

$12\left(x+4\right) \ = \ 8\left(2x+1\right) \\ \\ \rule{0.15cm}{0cm}12x+48 \ = \ 16x+8 \\ \\ \rule{1.1cm}{0cm} 4x \ = \ 40 \\ \\ \rule{1.3cm}{0cm} x \ = \ 10$ .