Find the equation of the line containing the following pair of points (-1,-7)(-4,-9)
To find the equation of a line given two points, you can use the formula for the slope-intercept form:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Let's label the points as follows:
Point 1: (-1, -7)
Point 2: (-4, -9)
Using the formula:
m = (-9 - (-7)) / (-4 - (-1))
m = (-9 + 7) / (-4 + 1)
m = -2 / -3
m = 2/3
So, the slope (m) is 2/3.
Step 2: Use the slope-intercept form to find the equation:
We have the slope (m = 2/3) and one of the points (Point 1: (-1, -7)). We can substitute these values into the equation:
y = mx + b
-7 = (2/3)(-1) + b
Simplify the equation:
-7 = -2/3 + b
To isolate b, add 2/3 to both sides:
-7 + 2/3 = b
-21/3 + 2/3 = b
-19/3 = b
So, the y-intercept (b) is -19/3.
Step 3: Write the final equation:
The equation of the line is:
y = (2/3)x - 19/3