Final Answer:
The equation of the line that passes through the point (0, -1/2) and has a slope of 3/4 is 3x - 4y = -2.
Step-by-step explanation:
o write an equation in point-slope form of a line, we can use the formula:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line.
In this case, the given point is (0, -1/2) and the slope is 3/4. Let's substitute these values into the formula:
y - (-1/2) = (3/4)(x - 0)
Simplifying the equation further:
y + 1/2 = 3/4x
To write the equation in a more standard form, we can clear the fractions by multiplying both sides by 4:
4(y + 1/2) = 4(3/4x)
4y + 2 = 3x
Finally, rearrange the equation to have the terms in standard order:
3x - 4y = -2
So, the equation of the line that passes through the point (0, -1/2) and has a slope of 3/4 is 3x - 4y = -2.