Algebra Help..?

Question

I have an algebra question and I would like someone to explain to me how to correctly do the question.The directions say write an equation of the line that is paralellel to the given line aand passes throught the given point. The equation is y=9x+6 and the given points are (6,9). Please explain. Thanks

Answer 1

Parallel lines have equal slopes. Since the slope pf the given line is 9, the slope of the new line is also 9. If the line passed through (6,9), you substitute 6 for x and 9 for y in the equation y = 9x +b.

9 = 9(6) + b so b = -45

So your equation is y = 9x - 45

Answer 2

The general equation for a straight line is y=mx+b where the slope is m and the y intercept is b (crosses the Y-axis). Any parallel line will have the same slope but will cross the Y-axis at a different point, say c. Now you know that all lines parallel to y=9x+6 will have the form y=9x+c. Given it must pass through the point (6,9) you can solve for c thus:
9=9(6)+c or c=-45

So the line you want is y=9x-45

Answer 3

Parallel lines have the same slope. So the equation of the line you are looking for has the same slope as the given line. The line has slope equal to 9. This can be determined since the line is in the familar y = mx + b form with the slope equal to m.

Thus the line you are looking for also has slope equal to 9, however the y-intercept, that is the "b" will have different value as determined by the point you have been given, here (6,9).

Using that in the equation y = 9x + b will determine b. That is,
9 = 9*6 + b or b = 9 - 54 = -45.

So the equation is: y = 9x - 45

Answer 4

so this is really easy.
If the equation of the line is y=9x+6
The line parallel to it will have the same slope.
Slope is always m in the equation y=mx+b
so y=9x+6 has an m or slope equal to 9
In our new equation must pass through the point (6,9)
x=6 and y=9. So now we have m=9, x=6, and y=9
We will put this information into the line finding equation which is...

(y-y(1))=m(x-x(1))
(9-y)=9(6-x) we substituite and distribute
9-y=54-9x let's get y by itself
-y=54-9-9x move that 9
-y=45-9x divide by negative 1 on both sides
y=-45+9x now let's rearrange
y=9x-45

y=9x-45 is the new line of the equation that passes throught the points (6,9) and is parallel to the line y=9x+6

Answer 5

Interpreting the form "y=mx + b", the slope "m" of the line 9x+6 is 9. So to find the slope of a line parallel to that, it also has to have a slope of 9. You can use point-slope form:

y - y1 = m(x - x1)

To get:
y - 9 = 9 (x - 6)
which, simplified, gives you the equation:
y = 9x - 45

Answer 6

Ok so in the original equation the slope is 9x right? so your new equation, to be parrallell has to have a slope of 9x. so your new equation would be y=9x-?. the equation y=9x passes through the point (6,54) so so go through (6,9) you need to take away 45 (54-45=9) so the new equation is y=9x-45.

Answer 7

9*6+6= 60, and we want 9, so subtract 51 to get:
9x-45

Answer 8

Use the point slope method to solve it.