Write the equation of the line through the point (2,1) and parallel to the equation y=3x+4

Mathematics

1 answer:

LenKa [72]3 years ago

4 0

Answer:

y = 3x - 5

Step-by-step explanation:

The equation is given in the form

y = 3x + 4

that is

y = mx + b

So, we can say:

m = 3

This is the slope (m).

Parallel lines have equal slopes, so we can say the line parallel will have the equation:

y = 3x + b

We are given that it passes through (2,1), so we plug in respective values of x and y and solve for b:

y = 3x + b

1 = 3(2) + b

1 = 6 + b

b = 1 - 6

b = -5

So, the equation is:

y = 3x - 5

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If Pentagon ABCDE was dilated to create Pentagon A'B'C'DE', what rule was used?

svetlana [45]

Answer:

<em>B</em> $(x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)$

Step-by-step explanation:

<u>Dilations</u>

Given a point A(x,y) and a scale factor k the dilated image of A, called A' is calculated as A'=(kx,ky), assuming the same scale factor is applied in both axes.

The pentagon ABCDE was dilated to create pentagon A'B'C'D'E'. To find the dilaton rule used, we must find two clear points where the coordinates of both axes can be easily read from the graph.

Point C(-2,0) maps to C'(-5,0). This gives us the scale factor for the x-axis of -5/(-2)= 5/2.

The y-coordinate of E is 2 and the y-coordinate of E' is 5. This gives us the same scale factor for the y-axis of 5/2.

Thus, the rule to dilate the pentagon is:

B $\mathbf{(x,y) \rightarrow \left(\frac{5}{2}x,\frac{5}{2}y\right)}$