Write in general form, the equation of the straight line that passes through the points A(-6, -1) and B(2,2)
(2+1)/(2+6) = (y+1)/(x+6)
3/8 = (y+1)/(x+6)
3 x + 18 = 8 y + 8
3 x - 8 y = -10
To find the equation of a straight line that passes through two points, you can use the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one point on the line, and m is the slope of the line.
First, let's find the slope (m) using the two points A(-6, -1) and B(2, 2):
m = (y2 - y1) / (x2 - x1)
= (2 - (-1)) / (2 - (-6))
= 3 / 8
Now we can substitute one of the points (A or B) and the slope (m) into the point-slope form:
Using point A(-6, -1):
y - (-1) = 3/8(x - (-6))
y + 1 = 3/8(x + 6)
y + 1 = 3/8x + 9/4
Finally, let's rearrange the equation into the general form:
8(y + 1) = 3x + 54/4
8y + 8 = 3x + 13.5
8y = 3x + 13.5 - 8
8y = 3x + 5.5
Therefore, the general form of the equation of the straight line passing through points A(-6, -1) and B(2, 2) is 8y = 3x + 5.5.
To find the equation of the straight line that passes through two points, A and B, we can use the point-slope form of a line equation: y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of one point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.
To determine the slope, m, of the line passing through points A(-6, -1) and B(2,2), we can use the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) are the coordinates of point A and (x₂, y₂) are the coordinates of point B.
Substituting the values into the formula:
m = (2 - (-1)) / (2 - (-6))
= 3 / 8
Now that we have the slope, we can choose either point A or B to substitute into the point-slope form. Let's use point B(2,2):
y - 2 = (3/8)(x - 2) [point-slope form]
Next, we will transform this equation into the general form, where the coefficient of x, y, and the constant term are integers and the coefficient of x is positive.
Distributing (3/8) to (x - 2):
y - 2 = (3/8)x - (3/8)(2)
y - 2 = (3/8)x - 3/4
Multiplying through by 8 to clear fractions:
8(y - 2) = 8(3/8)x - 8(3/4)
8y - 16 = 3x - 6
Rearranging the terms:
3x - 8y = -10
Hence, the equation of the straight line in general form that passes through points A(-6, -1) and B(2,2) is 3x - 8y = -10.