Write the equation of the line in standard form:
(-3, 6); m = 1/2
(1, 0) & (-5, 3)
(-5, -5) & (-1, 3)
I will do one:
(-3, 6); m = 1/2
y=mx+b
6=1/2 * (-3) + b
solve for b.
now standard form:
http://www.mathwarehouse.com/algebra/linear_equation/standard-form-equation-of-a-line.php
Ax+By=C
y=mx+b
you know m, b
y=1/2 x + b
2y=x+2b
x-2y=-2b put in b, and you have it.
To write the equation of a line in standard form, which is in the form Ax + By = C, we need the values of A, B, and C.
1) For the line with the point (-3, 6) and slope m = 1/2:
Step 1: Use the point-slope formula, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the coordinates and the slope, we have:
y - 6 = (1/2)(x - (-3))
y - 6 = (1/2)(x + 3)
y - 6 = (1/2)x + 3/2
Step 2: Simplify the equation.
2(y - 6) = x + 3 [Multiply both sides by 2 to eliminate the fraction]
2y - 12 = x + 3
x - 2y = -15 [Rearrange to standard form]
So, the equation of the line is x - 2y = -15.
2) For the line passing through points (1, 0) and (-5, 3):
Step 1: Find the slope using the formula: m = (y2 - y1) / (x2 - x1) [Let (x1, y1) = (1, 0) and (x2, y2) = (-5, 3)]
m = (3 - 0) / (-5 - 1)
m = 3 / -6
m = -1/2
Step 2: Use the point-slope formula with one of the points and the slope.
y - 0 = (-1/2)(x - 1)
y = (-1/2)(x - 1)
Step 3: Simplify the equation.
y = (-1/2)x + 1/2
Step 4: Rearrange to standard form.
2y = -x + 1 [Multiply both sides by 2 to eliminate the fraction]
x + 2y = 1
So, the equation of the line is x + 2y = 1.
3) For the line passing through points (-5, -5) and (-1, 3):
Step 1: Find the slope using the formula: m = (y2 - y1) / (x2 - x1) [Let (x1, y1) = (-5, -5) and (x2, y2) = (-1, 3)]
m = (3 - (-5)) / (-1 - (-5))
m = 8 / 4
m = 2
Step 2: Use the point-slope formula with one of the points and the slope.
y - (-5) = 2(x - (-5))
y + 5 = 2(x + 5)
Step 3: Simplify the equation.
y + 5 = 2x + 10
Step 4: Rearrange to standard form.
2x - y = -5
So, the equation of the line is 2x - y = -5.
To write the equation of a line in standard form (Ax + By = C), you need two pieces of information: the slope (m) and a point on the line (x1, y1).
1. (-3, 6); m = 1/2:
First, we can use the point-slope formula to find the equation of this line. The point-slope formula is y - y1 = m(x - x1).
Substitute the given values into the formula:
y - 6 = (1/2)(x - (-3))
y - 6 = (1/2)(x + 3)
y - 6 = (1/2)x + 3/2
To convert this equation to standard form, eliminate fractions by multiplying every term by 2:
2(y - 6) = 2(1/2)x + 2(3/2)
2y - 12 = x + 3
Rearrange the terms to bring them to the left side:
-x + 2y = 15
The equation of the line in standard form is -x + 2y = 15.
2. (1, 0) and (-5, 3):
To find the slope (m), use the formula: m = (y2 - y1) / (x2 - x1).
Substituting the given coordinates into the formula:
m = (3 - 0) / (-5 - 1)
m = 3 / -6
Simplify: m = -1/2
Now that we have the slope, we can use the point-slope formula:
y - y1 = m(x - x1)
Take the first point (1, 0):
y - 0 = (-1/2)(x - 1)
Simplify: y = (-1/2)x + 1/2
Next, convert the equation to standard form (Ax + By = C). Multiply every term by 2 to eliminate fractions:
2y = -x + 1
Rearrange: x + 2y = 1
The equation of the line in standard form is x + 2y = 1.
3. (-5, -5) and (-1, 3):
Similarly, we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = (3 - (-5)) / (-1 - (-5))
m = 8 / 4
Simplify: m = 2
Using the point-slope formula with the first point (-5, -5):
y - (-5) = 2(x - (-5))
Simplify: y + 5 = 2(x + 5)
y + 5 = 2x + 10
Rearrange and eliminate fractions:
2x - y = 5
The equation of the line in standard form is 2x - y = 5.