Find the equation of the line passing through the given points
(1,5) (2,7)
please show work
To find the equation of the line passing through two points, you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one of the points, and m is the slope of the line.
Step 1: Determine the slope (m)
The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.
Given points: (1,5) and (2,7)
Using the formula, we have m = (7 - 5) / (2 - 1) = 2/1 = 2.
Step 2: Choose a point and substitute values (x1, y1)
You can choose either of the two given points to substitute into the equation. Let's use the first point (1,5).
Substituting x1 = 1 and y1 = 5, we have the equation: y - 5 = 2(x - 1).
Step 3: Simplify the equation
Distribute 2 to (x - 1): y - 5 = 2x - 2.
Step 4: Rewrite the equation in standard form
Next, to convert the equation into standard form (Ax + By = C), move all terms to one side:
2x - y = 2 + 5.
Combine like terms: 2x - y = 7.
So, the equation of the line passing through the points (1,5) and (2,7) is 2x - y = 7.