# Thread: Determining equations of lines albebraically

1. ## Determining equations of lines albebraically

I'm stuck on these questions and I don't know how to solve.
With the same x- intercept as 3x-7x+12=0 and parallel to 6x+8y-5=0
I need to find the equation for this line.

Also I need the equation for this line.

With the same x-intercept as y=-2x+10 and perpendicular to 10x+4y+7=0

Please explain the formula on how you found the equation, thanks.

2. 6x + 8y - 5 = 0

These are applications of the slope-intercept form. Yo umust know a few things:

1) y = mx + b - This is the form
1a) m is the slope
1b) b is the y-intercept.
1c) it is important to note that the x-intercept is NOT given in this form.

2) Parallel lines have the same slope.
3) Perpendicular lines have slopes with this property (m1)*(m2) = -1

That is ALL you need for these.

Put them in slope-intercept form, if possible

3x - 7x + 12 = 0 ==> x = 3
6x + 8y - 5 = 0 ==> y = -(3/4)x + (5/8)

Now the instructions:

Here's the line: y = mx + b
1) Same x-intercept as the first. ==> 0 = m(3) + b ==> b = -3m
Here's the line: y = mx - 3m
2) Parallel to the second: m = -3/4
Here's the line: y = (-3/4)x - 3(-3/4) = -(3/4)x + 9/4

You do the next one.

Note: I took the problem as presented. If there are typos, you'll get to work the real problem and show us how you did! :-)

3. First find the x-intercept of this equation

Originally Posted by buck
With the same x- intercept as 3x-7x+12=0 $\displaystyle {\color{red}\text{should there be a 'y' here somewhere?}}$

Then find the gradient of this line by transposing to $\displaystyle y=mx+c$

Originally Posted by buck
6x+8y-5=0

4. Give me a sec teachers, I'm like brain blast.