Answer:
Explanation:
To write the equation of the line that passes through the points (3, -4) and (7, 6), we can follow these steps:
Step 1: Find the slope of the line
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Plugging in the given values, we get:
slope = (6 - (-4)) / (7 - 3)
slope = 10 / 4
slope = 5 / 2
Step 2: Use point-slope form to write the equation of the line
Point-slope form of a line with slope m passing through a point (x1, y1) is given by:
y - y1 = m(x - x1)
We can use either of the given points to write the equation. Let's use (3, -4):
y - (-4) = (5/2)(x - 3)
Simplifying this equation, we get:
y + 4 = (5/2)x - (15/2)
Subtracting 4 from both sides, we get:
y = (5/2)x - (23/2)
This is the equation of the line in point-slope form.
Step 3: Simplify the equation if it is not in point-slope form
The equation we obtained in step 2 is already in point-slope form, so we do not need to simplify it any further.
Note: If the line was horizontal (i.e., it had zero slope), then its equation would be y = constant, where the constant is the y-coordinate of any point on the line. If the line was vertical (i.e., its slope was undefined), then its equation would be x = constant, where the constant is the x-coordinate of any point on the line.