42.1k views
5 votes
Find the equation of the line passing through the points (1,4) and (6,14) and the line passing through the points (1,-2) and (6,23).

1 Answer

6 votes

Final answer:

To find the equation of a line passing through two points, use the point-slope formula. The slope is found using the formula (y2 - y1) / (x2 - x1). Substitute the slope and the coordinates of one point into the point-slope formula to find the equation of the line.

Step-by-step explanation:

To find the equation of a line passing through two points, we can use the point-slope formula: y - y1 = m(x - x1). First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). For the first set of points (1, 4) and (6, 14), the slope is: m = (14 - 4) / (6 - 1) = 10/5 = 2. Second, we can choose either point and substitute its coordinates into the point-slope formula, along with the slope, to find the equation of the line. Let's use the point (1, 4): y - 4 = 2(x - 1). Simplifying gives us: y - 4 = 2x - 2. Rearranging the equation gives us the final equation of the line: y = 2x + 2. Let's follow the same steps for the second set of points (1, -2) and (6, 23).

User James Jeffery
by
7.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories