What would these be in (y - k = m(x - h)) form?
1. Slope = ½; (h, k) = (1, -2)
2. Slope equals 2 and the line goes through the point (-1, 3)
3. The line goes through the points (8,5) and (9, 6)
your point-slope form
y - k = m(x - h)
1. you are given all the necessary data, m = 1/2, point is (1, -2)
y + 2 = (1/2)(x-1)
I would multiply both sides by 2 to get rid of fractions
2y + 4 = x - 1
arrange into whichever form you like
2. same thing
3. first find the slope, then same thing
1. y+2 = 1/2(x-1).
2. Same procedure as #1.
3. (8, 5), (9, 6), (x, y).
m = (6-5)/(9-8) = 1.
y-5 = 1(x-8).
To write the equation in the form y - k = m(x - h), you need to find the values of m (slope) and (h, k) (the point through which the line passes).
1. Slope = 1/2; (h, k) = (1, -2):
In this case, the slope (m) is already given as 1/2, and the point (h, k) is (1, -2).
Therefore, the equation can be written as y - (-2) = (1/2)(x - 1) or y + 2 = (1/2)(x - 1).
2. Slope equals 2, and the line goes through the point (-1, 3):
Given the slope (m) as 2 and the point (h, k) as (-1, 3), you can substitute these values into the equation y - k = m(x - h).
Therefore, the equation can be written as y - 3 = 2(x - (-1)) or y - 3 = 2(x + 1).
3. The line goes through the points (8,5) and (9, 6):
To find the slope (m), use the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) = (8, 5) and (x2, y2) = (9, 6).
m = (6 - 5)/(9 - 8) = 1/1 = 1.
The slope (m) is 1.
To find the point (h, k), choose one of the given points (8, 5) or (9, 6).
Let's choose the point (8, 5).
Substituting the values of m, h, k into the equation y - k = m(x - h), we get y - 5 = 1(x - 8).
Therefore, the equation is y - 5 = x - 8.
By following these steps, you can convert given information into the desired format y - k = m(x - h).