Mathematics, 15.07.2019 02:10 Lujfl

Which of the following equations represents a line that is parallel to y = 3x +2
and passes through the point, (1,6)?

Answers: 2

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Answer from: suieemage

y=3x+3 is slope-intercept form

y-6=3(x-1) is point-slope form

I don't know the form your equation(s) are in. There are other forms.

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

So the slope of y=3x+2 is 3.

Parallel lines have the same slope. So the slope of the line we are looking for has a slope of 3.

Therefore, our equation his this form y=3x+b.

We need to now find b.

We know a point (x,y) on the line.

y=3x+b using (x,y)=(1,6).

6=3(1)+b

6=3+b

Subtract 3 on both sides:

3=b

So the equation is y=3x+3

Point-slope form is another form we can put our line into

y-y1=m(x-x1)

where m is the slope and (x1,y1) is a point on the line.

We have m=3 and a point (x1,y1) on the line is (1,6).

y-6=3(x-1)

Answer from: nmartin1467

$\huge{\boxed{y=3x+3}}$

It could also be $\boxed{y-6=3(x-1)}$

We can use point-slope to find this. Parallel lines have the same slope, and the given line has a slope of 3 ( in y=mx+b ). This means that the parallel line will also have a slope of 3.

Point-slope form is y-y_1=m(x-x_1) , where is the slope and (x_1, y_1) is a known point on the line.

Plug in the values. $\boxed{y-6=3(x-1)}$ (point-slope form)

Distribute. y-6=3x-3

Add 6 to both sides. $\boxed{y=3x+3}$ (slope-intercept form)

Answer from: Quest

step-by-step explanation:

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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Which of the following equations represents a line that is parallel to y = 3x +2
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