A line passes through (7, –6) and (8, –5).
To find the equation of the line passing through the points (7, -6) and (8, -5), we can use the point-slope formula or slope-intercept form.
1. Using the point-slope formula:
The formula for the equation of a line in point-slope form is: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Let's use the point (7, -6):
y - (-6) = m(x - 7)
y + 6 = m(x - 7)
Now, let's find the slope (m):
The slope (m) is given by the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
Using the two given points (7, -6) and (8, -5):
m = (-5 - (-6))/(8 - 7)
m = (-5 + 6)/(8 - 7)
m = 1/1
m = 1
Substituting the slope (m) into the point-slope formula, we get:
y + 6 = 1(x - 7)
y + 6 = x - 7
Simplifying the equation, we get:
y = x - 13
So, the equation of the line passing through the points (7, -6) and (8, -5) is y = x - 13.
Alternatively, we can also solve using the slope-intercept form:
2. Using the slope-intercept form:
The slope-intercept form of a line is: y = mx + b, where m is the slope of the line and b is the y-intercept.
Let's find the slope (m) as we did before: m = 1.
Using the point (7, -6), we can substitute the values into the equation:
-6 = 1(7) + b
-6 = 7 + b
Solving for b, we get:
b = -6 - 7
b = -13
So, the equation of the line passing through the points (7, -6) and (8, -5) using the slope-intercept form is:
y = x - 13.