I have an assignment to write an equation to point-slope form, then to standard form, and then to slope-intercept form. I have used the points (-2,-1) or (1,2), but I used (-2,-1).
Now, I have the point-slope form of y + 1= 1(x + 2) and the standard form of y – 1x = -1. When I convert into slope-intercept form, I am getting the slope as -1, which is the problem. Could someone please tell me where I am going wrong?
Actually, the slope is not -1, but the y-intercept comes up as -1.
your slope is correct as +1
your equation of
y+1 = 1(x+2) is also correct
then y+1 = x+2
y = x+1 ---> slope-yintercept form
y-x = 1
x - y = -1 ----> standard form ( I multiplied each term by -1)
So, how did you multiply the terms by -1?
And how do you rewrite x - y = -1 into slope-intercept form?
in standard form we usually lead with the x term with a positive coefficient, so I wanted a +x as my first term, it was -x .
to change a standard form to slope- yintercept form usually takes 2 steps:
1. move all terms except the y term to the right
e.g.
4x - 5y = 8 ---≥ -5y = -4x + 8
2. divide each term by the coefficient of the y term
-5y = -4x + 8 ----> y = (-4/-5)x + 8/-5
y = (4/5)x - 8/5 , just an example, has nothing to do with your question
apply those 2 steps to your question.
To convert the equation from point-slope form to standard form, you need to make sure that all the variables are on one side of the equation and the constant term is on the other side.
Let's start with the given equation in point-slope form: y + 1 = 1(x + 2).
To convert it to standard form, we first distribute the 1 to the terms inside the parentheses:
y + 1 = x + 2.
Next, we subtract x from both sides to isolate y:
y - x + 1 = 2.
Finally, to rearrange it into the standard form, we move the constant term to the right side by subtracting 1 from both sides:
y - x = 2 - 1,
y - x = 1.
So, the equation in standard form is y - x = 1.
Now let's convert it to slope-intercept form. In slope-intercept form, the equation is written as y = mx + b, where m represents the slope and b is the y-intercept.
To convert the equation from standard form to slope-intercept form, you need to solve for y.
Taking the standard form equation y - x = 1, we can add x to both sides:
y = x + 1.
Now the equation is in slope-intercept form. We can see that the slope, represented by m, is 1, not -1 as you mentioned.
Therefore, the correct slope-intercept form of the equation is y = x + 1.
To avoid errors, always double-check your calculations during the conversion process.