Question

Write the equation of the line that passes through the points (7, 4) and (1, 2). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.​

Answer 1

The equation of the line passing through (7, 4) and (1, 2) in point-slope form is y = (1/3)x + (5/3).

Step-by-step explanation:

To find the equation of the line passing through two given points, we can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one point and m is the slope of the line.

First, calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (7, 4) and (x2, y2) = (1, 2).

m = (2 - 4) / (1 - 7) = (-2) / (-6) = 1/3.

Now that we have the slope, choose one of the given points, let's say (7, 4), and substitute it into the point-slope formula:

y - y1 = m(x - x1)

y - 4 = (1/3)(x - 7)

y - 4 = (1/3)x - 7/3

To express the equation in fully reduced point-slope form, isolate y:

y = (1/3)x - 7/3 + 4

y = (1/3)x - 7/3 + 12/3

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

Therefore, the equation of the line passing through the points (7, 4) and (1, 2) in point-slope form is y = (1/3)x + 5/3. This equation represents a line with a slope of 1/3 that passes through the given points.

Answer 2

The equation of the line passing through the points (7, 4) and (1, 2) is y - 4 = (1/3)(x - 7).

Step-by-step explanation:

The equation of the line that passes through the points (7, 4) and (1, 2) can be found using the point-slope form of a linear equation. The formula for the point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of one of the points and m is the slope of the line.

First, let's find the slope using the formula: m = (y₂ - y₁) / (x₂ - x₁). Plugging in the values, we get m = (2 - 4) / (1 - 7) = -2 / -6 = 1/3.

Now, we can choose one of the points, for example, (7, 4), and plug it into the point-slope form to find the equation of the line:

y - 4 = (1/3)(x - 7)

This is the equation in point-slope form for the line passing through the given points.