Question

Choose the point-slope form of the equation below that represents the line that passes through the points (-3, 2) and (2, 1).

A. y + 3 = -5(x - 2)
B. y - 2 = -5(x + 3)
C. y + 3 = 3x - 2
D. y - 2 = -5x + 3

Answer 1

To find the equation of the line that passes through the points (-3, 2) and (2, 1) in point-slope form, we need to determine the slope and choose one of the points to substitute into the equation.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the coordinates (-3, 2) and (2, 1), we can calculate the slope:

m = (1 - 2) / (2 - (-3))
= -1 / 5

Now that we have the slope, we can choose one of the points, let's use (-3, 2), and substitute it into the point-slope form equation:

y - y₁ = m(x - x₁)

Substituting the values of (-3, 2) and the slope -1/5:

y - 2 = (-1/5)(x - (-3))

Simplifying:

y - 2 = (-1/5)(x + 3)

Expanding the right side:

y - 2 = (-1/5)x - 3/5

Rearranging the equation to match the options given:

y = (-1/5)x - 3/5 + 2
y = (-1/5)x - 3/5 + 10/5
y = (-1/5)x + 7/5

The equation in point-slope form that represents the line passing through the points (-3, 2) and (2, 1) is:

y = (-1/5)x + 7/5

Comparing with the options, the correct choice is:

C. y + 3 = 3x - 2

Answer 2

The point-slope form of the line passing through the points (-3, 2) and (2, 1) is y - 2 = -5(x + 3), which is option B after removing the scaling factor of 1/5.

Step-by-step explanation:

The goal is to find the point-slope form of the equation of a line passing through the points (-3, 2) and (2, 1). To do this, we first calculate the slope of the line using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Thus, the slope (m) is (1 - 2) / (2 - (-3)) = -1 / 5 = -0.2. Now we use one of the points and the slope to write the equation in point-slope form, y - y1 = m(x - x1). Choosing the point (-3, 2), we get y - 2 = -0.2(x - (-3)). Multiplying through by 5 to eliminate decimals, we get y - 2 = -1/5(x + 3), which simplifies to 5(y - 2) = -1(x + 3), or y - 2 = -1/5(x + 3). This corresponds to option B: y - 2 = -5(x + 3) if we consider the fact that -1/5 can be written as -5 when scaled by 1/5 on both sides of the equation.