Find an equation of the line containing the given pair of points.
(-3, -2), and (-8,-5)
The equation of the line in slope-intercept form is y= what
Well, there are several ways but you want y = m x + b
so
-2 = m (-3) + b
b = (3 m-2) use (3m-2) for b in the other point
-5 = m (-8) + b
-5 = -8 m + 3 m - 2
5 m = 3
m = 3/5
then b = 3 (3/5) - 2
b = 9/5 - 10/5 = -1/5
so
y = (3/5) x - 1/5
or
5 y = 3 x - 1
To find the equation of a line containing two given points, we can use the slope-intercept form of the equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
The first step is to calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the given points into the formula:
m = (-5 - (-2)) / (-8 - (-3))
m = (-5 + 2) / (-8 + 3)
m = -3 / -5
m = 3/5
Now that we know the slope (m = 3/5), we can substitute it into the slope-intercept form equation (y = mx + b) and choose one of the points to find the value of b.
Let's choose the first point (-3, -2):
-2 = (3/5)(-3) + b
-2 = -9/5 + b
To find the value of b, let's add 9/5 to both sides of the equation:
-2 + 9/5 = -9/5 + b + 9/5
(-10/5) + (9/5) = -9/5 + b + 9/5
-1/5 = b
Therefore, b = -1/5.
Now we have the slope (m = 3/5) and the y-intercept (b = -1/5).
The equation of the line in slope-intercept form is:
y = (3/5)x - 1/5.