Question

Which equation shows the point-slope form of the line that passes through (3, 2) and has a skope of 1/3 ?

A) y + 2 = 1/3 * (x + 3)
B)y - 2 = 1/3 * (x - 3)
C)y + 3 = 1/3 * (x + 2)
D)y - 3 = 1/3 * (x - 2)

Answer 1

The equation that represents the line passing through (3, 2) with a slope of 1/3 is y = 1/3x + 1.

Step-by-step explanation:

The point-slope form of a linear equation is given by the equation y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. In this case, we have the point (3, 2) and a slope of 1/3. To find the equation that represents this line, we substitute the values into the point-slope form:

y - 2 = 1/3(x - 3)

Now, let's simplify the equation:

y - 2 = 1/3x - 1

Adding 2 to both sides, we get:

y = 1/3x + 1

Therefore, the correct equation in point-slope form is y = 1/3x + 1, which corresponds to option A.