What would these be in (y - k = m(x - h)) form?
1. Slope = ½; (h, k) = (1, -2)
a. 2y+4=x-1
2. Slope equals 2 and the line goes through the point (-1, 3)
a. y-3=2(x-(-1)
3. The line goes through the points (8,5) and (9, 6)
a. y-5=1(x-8)
4. The line goes through the points (-1, -7) and (-8, -2)
a. y-(-7)-5/7(x-(-1)
Are my answers correct? I wasn't 100% about 2 and 4. Thank you!
you wrote: y-(-7)-5/7(x-(-1)
I hope you meant
y + 7 = (-5/7)(x + 1)
They are all correct, expecting you to clean up those equations a bit
To determine if your answers are correct, let's convert each equation into the "y - k = m(x - h)" form and compare them:
1. Slope = ½; (h, k) = (1, -2)
To convert the equation "2y+4=x-1" into the desired form, let's rearrange it:
2y + 4 = x - 1
2y = x - 5
y = (1/2)x - (5/2)
Now, let's compare this with the desired form "y - k = m(x - h)":
y - (-2) = (1/2)(x - 1)
y + 2 = (1/2)(x - 1)
Thus, the correct equation in the desired form for this scenario is "y + 2 = (1/2)(x - 1)", which is different from your answer.
2. Slope equals 2, and the line goes through the point (-1, 3)
To convert the equation "y-3=2(x-(-1))" into the desired form, let's simplify it:
y - 3 = 2(x + 1)
y - 3 = 2x + 2
y = 2x + 5
Now, let's compare this with the desired form "y - k = m(x - h)":
y - 5 = 2(x - (-1))
y - 5 = 2(x + 1)
In this case, your original answer "y-3=2(x-(-1))" is actually in the desired form and is correct.
3. The line goes through the points (8,5) and (9, 6)
To find the slope between these two points, we use the formula:
Slope (m) = (change in y) / (change in x)
m = (6 - 5) / (9 - 8)
m = 1
Using the point-slope form, let's convert the equation into the desired form:
y - 5 = 1(x - 8)
This matches your original answer, so it is correct.
4. The line goes through the points (-1, -7) and (-8, -2)
Similarly, let's find the slope between these two points:
m = (-2 - (-7)) / (-8 - (-1))
m = 5 / -7
m = -5/7
Using the point-slope form, let's convert the equation into the desired form:
y -(-7) = (-5/7)(x -(-1))
y + 7 = (-5/7)(x + 1)
In this case, your original answer "y-(-7)-5/7(x-(-1))" is not quite correct. The correct form would be "y + 7 = (-5/7)(x + 1)".
To recap, the correct equations in the desired form are:
1. y + 2 = (1/2)(x - 1)
2. y - 3 = 2(x - (-1)) (or y - 3 = 2(x + 1))
3. y - 5 = 1(x - 8)
4. y + 7 = (-5/7)(x + 1)
I hope this explanation helps! Let me know if you have any further questions.