So, I've got these problems:
To tell which form the equation is in.
1)2x+8y=-3
I think this one is standard form.
2)y=-5x+8
I think this is slope intercept form.
3)y+4=2(x-6)
I think this is also slope intecept form.
Could somebody tell me if my answers are correct, if not explain why it's not?
Thanks
(1), (2) correct.
(3) This is the point-slope form, i.e.
(y-y1)=m(x-x1)
represents a line that passes through point (x1,y1) with a slope of m.
You are partially correct and partially incorrect. Let me explain why.
1) 2x + 8y = -3
You are correct, this equation is indeed in standard form. Standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
2) y = -5x + 8
You are correct again! This equation is in slope-intercept form. Slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
3) y + 4 = 2(x - 6)
Now, the equation you provided is not in slope-intercept form. It is in a different form called point-slope form. Point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
To convert this equation to slope-intercept form, we can follow these steps:
1. Distribute the 2 on the right side: y + 4 = 2x - 12
2. Bring all the terms with y to one side: y = 2x - 12 - 4
3. Simplify: y = 2x - 16
So, the correct form of this equation is indeed slope-intercept form.
To summarize:
1) 2x + 8y = -3 - Standard form
2) y = -5x + 8 - Slope-intercept form
3) y = 2x - 16 - Slope-intercept form
I hope this clears up any confusion. Let me know if you have any further questions!