What is the slope-intercept form of the equation that represents the line passing through the points (2, 3) and (-5, 1)?
To find the slope-intercept form of the equation of a line passing through two given points, you can follow these steps:
Step 1: Find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope using the given points (2, 3) and (-5, 1):
m = (1 - 3) / (-5 - 2)
m = -2 / -7
m = 2/7
Step 2: Now that we have the slope (m), we can use the slope-intercept form of a line, which is:
y = mx + b
Step 3: Substitute the slope (m) and one of the given points (x, y) into the equation, and solve for the y-intercept (b).
Using the point (2, 3):
3 = (2/7)(2) + b
3 = 4/7 + b
b = 3 - 4/7
b = 21/7 - 4/7
b = 17/7
Step 4: Finally, substitute the slope (m) and the y-intercept (b) into the slope-intercept form equation:
y = (2/7)x + 17/7
Therefore, the slope-intercept form of the equation representing the line passing through the points (2, 3) and (-5, 1) is:
y = (2/7)x + 17/7