Write an equation of the line passing through each of the following pairs of points.
(5, 7), (−6, −3)
To write an equation of the line passing through two points, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
Where:
- m is the slope of the line
- b is the y-intercept of the line
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope first using the given points (5, 7) and (-6, -3):
m = (-3 - 7) / (-6 - 5)
m = (-3 - 7) / (-11)
m = (-10) / (-11)
m = 10/11
Now that we have the slope, we can substitute it into the slope-intercept form equation along with one of the points to find the y-intercept (b).
Using point (5, 7):
7 = (10/11)(5) + b
Simplifying:
7 = 50/11 + b
To isolate b, subtract 50/11 from both sides:
7 - 50/11 = b
To perform the subtraction:
(77 - 50) / 11 = b
Simplifying:
27 / 11 = b
b ≈ 2.45 (rounded to two decimal places)
So, the equation of the line passing through the points (5, 7) and (-6, -3) is:
y = (10/11)x + 2.45
(5,7), (-6, -3).
y = mx + b.
m = (-3-7)/(-6-5) = 10/11
b = y-mx = 7-(10/11)*5 = 27/11.
y = (10/11)x + 27/11.
find the slope
write the equation in point-slope form