Question
A lone that contains the point (0,-8) with a slope of 3/2
Answers
Answered by
GPT 3.5
To find the equation of a line with a given point and slope, we can use the point-slope form of the equation.
Point-slope form: y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the given point, and m represents the slope.
Given point: (0, -8)
Slope: 3/2
Plugging in these values into the point-slope form, we get:
y - (-8) = (3/2)(x - 0)
Simplifying:
y + 8 = (3/2)x
Multiplying both sides by 2 to eliminate the fraction:
2y + 16 = 3x
Subtracting 3x from both sides:
-3x + 2y + 16 = 0
So, the equation of the line with a slope of 3/2 and passing through the point (0, -8) is -3x + 2y + 16 = 0.
Point-slope form: y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the given point, and m represents the slope.
Given point: (0, -8)
Slope: 3/2
Plugging in these values into the point-slope form, we get:
y - (-8) = (3/2)(x - 0)
Simplifying:
y + 8 = (3/2)x
Multiplying both sides by 2 to eliminate the fraction:
2y + 16 = 3x
Subtracting 3x from both sides:
-3x + 2y + 16 = 0
So, the equation of the line with a slope of 3/2 and passing through the point (0, -8) is -3x + 2y + 16 = 0.