Which is an equation of the line with a slope of 12 that passes through the point (3,−1)?
The equation of a line with slope m that passes through the point (x₁, y₁) is given by the equation:
y - y₁ = m(x - x₁)
In this case, the slope is 12 and the point is (3, -1). Substituting these values into the equation, we have:
y - (-1) = 12(x - 3)
Simplifying:
y + 1 = 12x - 36
Subtracting 1 from both sides:
y = 12x - 37
Therefore, the equation of the line with a slope of 12 that passes through the point (3, -1) is y = 12x - 37.
To find the equation of a line with a given slope that passes through a given point, you can use the point-slope form of the equation of a line.
The point-slope form is given by:
y - y₁ = m(x - x₁)
Where:
- y and x are variables representing the coordinates of any point on the line.
- y₁ and x₁ are the coordinates of the given point on the line.
- m is the slope of the line.
In this case, the slope (m) is given as 12, and the given point is (3, -1).
Substituting these values into the point-slope form equation, we get:
y - (-1) = 12(x - 3)
Simplifying:
y + 1 = 12(x - 3)
Expanding the brackets:
y + 1 = 12x - 36
Finally, rearranging the equation to the slope-intercept form (y = mx + b):
y = 12x - 37
Therefore, the equation of the line with a slope of 12 that passes through the point (3, -1) is y = 12x - 37.