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Solnce55 [7]
3 years ago
8

The given line passes through the points (0, −3) and (2, 3).

Mathematics
2 answers:
Alex Ar [27]3 years ago
8 0
Well, parallel lines have the same exact slope, so hmmm what's the slope of the one that runs through <span>(0, −3) and (2, 3)?

</span>\bf \begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&&(~ 0 &,& -3~) &#10;%  (c,d)&#10;&&(~ 2 &,& 3~)&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope =  m\implies &#10;\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-(-3)}{2-0}\implies \cfrac{3+3}{2-0}\implies 3
<span>
so, we're really looking for a line whose slope is 3, and runs through -1, -1

</span>\bf \begin{array}{ccccccccc}&#10;&&x_1&&y_1\\&#10;%  (a,b)&#10;&&(~ -1 &,& -1~)&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope =  m\implies 3&#10;\\\\\\&#10;% point-slope intercept&#10;\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-1)=3[x-(-1)]&#10;\\\\\\&#10;y+1=3(x+1)<span>
</span>
Soloha48 [4]3 years ago
5 0

we know that

If two lines are parallel, then their slopes are the same

Step 1

<u>Find the slope of the given line</u>

Let

A(0,-3)\\B(2,3)

we know that

the formula to calculate the slope between two points is equal to

m=\frac{(y2-y1)}{(x2-x1)}

substitute the values in the formula

mAB=\frac{(3+3)}{(2-0)}

mAB=\frac{(6)}{(2)}

mAB=3

Step 2

<u>Find the equation of the parallel line in the point slope form</u>

we know that

m=3\\Point (1,-1)

the equation of the line in the point-slope form is equal to

y-y1=m*(x-x1)

substitute the values

y+1=3*(x+1)

therefore

<u>the answer is</u>

the equation in the point slope form is

y+1=3*(x+1)


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