Question

Determine the point-slope form of a line that passes through the points (1,10) and (3,16).

A) (y−10)=3(x−1)

B) (y+10)=3(x+1)

C) (y−10)=1/3​(x−1)

Answer 1

The point-slope form of a line passing through (1,10) and (3,16) is found by calculating the slope and using one of the given points, which results in the equation (y - 10) = 3(x - 1).

Step-by-step explanation:

The student was asked to determine the point-slope form of a line passing through the points (1,10) and (3,16). To find the equation in point-slope form, one must first calculate the slope of the line (m) using the two given points. The slope is found by dividing the difference in the y-coordinates by the difference in the x-coordinates. Once the slope is determined, the point-slope form equation y - y1 = m(x - x1) can be used, where (x1, y1) is one of the given points.

Let's calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1).

By plugging in the coordinates of the given points:

m = (16 - 10) / (3 - 1)

m = 6 / 2

m = 3.

The slope is 3. Now, using the point (1,10) and the slope of 3, the point-slope form of the line equation becomes:

(y - 10) = 3(x - 1).

Therefore, the correct option is:

A) (y - 10) = 3(x - 1)