what is the standard from of a point that passes through 4,12 and has a slope of 3/2
To find the equation of a line in standard form, we can use the point-slope form of a line, which is:
(y - y₁) = m(x - x₁)
where (x₁, y₁) represents the coordinates of the given point and m represents the slope of the line.
Given that the point passes through (4,12) and has a slope of 3/2, we can substitute these values into the point-slope form:
(y - 12) = (3/2)(x - 4)
Next, we multiply through by 2 to eliminate the fraction:
2(y - 12) = 3(x - 4)
Expanding both sides:
2y - 24 = 3x - 12
Rearranging the equation to have the standard form:
3x - 2y = -12 + 24
Simplifying:
3x - 2y = 12
Therefore, the standard form of the equation for a line passing through the point (4,12) with a slope of 3/2 is 3x - 2y = 12.