Answer:
Explanation:
To find the equation of a line in point-slope form using two given points, we can follow these steps:
1. Identify the coordinates of the given points. In this case, the points are (2,8) and (6,10).
2. Determine the slope of the line using the formula: slope (m) = (change in y) / (change in x). To calculate the change in y, subtract the y-coordinate of the first point from the y-coordinate of the second point. Similarly, subtract the x-coordinate of the first point from the x-coordinate of the second point to calculate the change in x.
For the given points (2,8) and (6,10), the change in y is 10 - 8 = 2, and the change in x is 6 - 2 = 4.
So, the slope (m) = 2 / 4 = 1/2.
3. Choose one of the given points, let's say (2,8), and plug in its coordinates along with the slope into the point-slope form equation: y - y₁ = m(x - x₁). Here, (x₁, y₁) represents the coordinates of the chosen point.
Using the point (2,8), the equation becomes: y - 8 = (1/2)(x - 2).
4. Simplify the equation if needed. In this case, the equation is already in point-slope form and does not require further simplification.
Thus, the equation of the line in point-slope form for the given points (2,8) and (6,10) is: y - 8 = (1/2)(x - 2).
(HERE IS ANOTHER EXAMPLE)
To find the equation of a line in point-slope form using two given points, we can follow these steps:
1. Begin with the formula for the point-slope form: y - y₁ = m(x - x₁), where (x₁, y₁) represents one of the given points, and m is the slope of the line.
2. Calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₂, y₂) represents the other given point.
3. Substitute the values of the slope (m) and one of the given points (x₁, y₁) into the point-slope formula.
4. Simplify the equation to obtain the final equation in point-slope form.
For the given points (2, 8) and (6, 10), let's apply these steps:
Step 1: Point-slope form: y - y₁ = m(x - x₁)
Step 2: Slope (m) = (10 - 8) / (6 - 2) = 2 / 4 = 1/2
Step 3: Substitute the values into the point-slope formula:
y - 8 = (1/2)(x - 2)
Step 4: Simplify the equation:
y - 8 = (1/2)x - 1
This is the equation of the line in point-slope form for the given points: y - 8 = (1/2)x - 1.