Find eqn w/ same y-int as y+12x+2=0 & is parallel to 7x-3y=-9

[cypeherenter]

Please help with solving this, and showing how its done.

Find an equation of the line that (a) has the same y-intercept as the line y+12x+2=0 and (b) is parallel to the line 7x-3y=-9.

Write your answer in the form y=mx+b.

 

[Deleted member 4993]

Find an equation of the line that (a) has the same y-intercept as the line y+12x+2=0y+12x+2=0 and (b) is parallel to the line 7x−3y=−97x-3y=-9.

Write your answer in the form y=mx+by=mx+b.

What are your thoughts?

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[Steven G]

Please help with solving this, and showing how its done.

Find an equation of the line that (a) has the same y-intercept as the line y+12x+2=0 and (b) is parallel to the line 7x-3y=-9.

Write your answer in the form y=mx+b.

So you just need m and b and you are done.

You are told this eq you are looking for has the same y-intercept as y+12x+2=0.

A y-intercept is always a point on the y-axis (after all it intercepts it). Every point has an x and y value associated with it. If a point is on the y axis do you know it's x or y value? You do know one of them--which one and what is its value?

You know the eq you are looking for is parallel to 7x-3y=-9. What do you know about parallel line and slopes? If you do not know then just think about what a slope of a line means (if you need to then look up the meaning of the slope of a line) and what it takes for two lines to be parallel.

 

[hoosie]

Finding equation of straight line using m and c


Example:

Find the equation of a straight line which runs parallel to the line 3y - 4x + 12 = 0 and has the same y-intercept as 5x + 8y - 20 = 0.
This question relies on your knowledge of the general equation of a straight line:
y = mx + c where m = slope, c = y-intercept
Remember that parallel lines have the same slope.


Step 1: Determine slope of: 3y - 4x + 12 = 0
Rearrange equation to make y the subject:
3y - 4x + 12 = 0
Adding 4x to both sides, subtracting 12 from both sides:
3y = 4x -12
Dividing both sides by 3:
y = 4x/3 - 4
Compare to general equation y = mx + c:
m = 4/3 c = -4


Step 2: Find y-intercept of: 5x + 8y - 20 = 0
Remember equation of y-axis is x = 0
Let x = 0:
5(0) + 8y - 20 = 0
8y = 20
y = 2.5
y-intercept: c = 2.5

Step 3: Use values for m and c to work out equation of straight line.
General equation: y = mx + c
Substitute: m = 4/3 c = 2.5
y = 4x/3 + 5/2
Multiply both sides by 6:
6y = 8x + 15
6y - 8x -15 = 0

Compare the two parallel lines:
y = 4x/3 - 4
y = 4x/3 + 5/2
Notes:
For each straight line coefficient of x = 4/3 - this is the gradient (m).
If the line y = 4x/3 - 4 is shifted up 6.5 units it will coincide with line y = 4x/3 + 5/2.
You can check your answer by graphing both straight lines on the same set of axes:

 

[HallsofIvy]

Please help with solving this, and showing how its done.

Find an equation of the line that (a) has the same y-intercept as the line y+12x+2=0 and (b) is parallel to the line 7x-3y=-9.

Write your answer in the form y=mx+b.

What do you know about this question? Do you know what "y-intercept" means? If you do what is the y-intercept of y+ 12x+ 2= 0? Do you know how to tell whether two lines, given in this way, or in the form y= mx+ b, are parallel? Can you write y+ 12x+ 2= 0 in that form?