Mathematician sisios

Question

A line passes through point (-6,-8) and has a slope of 4.

Write an equation in Ax+By=C form for this line.

Answer 1

Hi Danna,

I'll be glad to help! I think the simplest way to solve this problem is to start with the point of slope form of a linear equation:

1) y - y1 = m( x - x1) , where (x1,y1) is the point through which the line pass through, and m is the slope of the line

2) y - (-8)=4(x-(-6))

3) y+8=4(x+6)

4) y+8=4x +24

5) Now, you can subtract 24 from both sides,

y+8-24=4x+24-24

y-16=4x

5) Since you want the final formula to be Ax+By=C, so you need to have X and Y on the same side.

So, you can subtract y from both sides,

y-y-16=4x-y

-16=4x-y , Or 4x-y= -16

I hope this helps! Please let me know if you have any more questions.

Answer 2

Hi Danna,

To get this equation, it is probably easiest to write an equation in slope-intercept form first. This is a classic algebra equation: y=Mx + b where:

y=y-coordinate given

m=slope

x=x-coordinate given

b=y-intercept, where line crosses y-axis

For this problem:

y=-8

x=-6

m=4

Solve for b:

-8=4(-6) + b

-8= -24 + b

b=16

Slope-Intercept Equation:

y=4x+16

But we’re not done yet. Your problem requested the general form Ax+By=C where A, B, and C are real number constants, so we need to manipulate our point-slope equation into this form.

y=4x+16

Subtract y from both sides:

4x-y+16=0

Subtract 16 from both sides:

4x-y= -16

This is the general form, so this is your final answer. I hope this helps.