I need help finding an equation of the line containg (-5,-9)and (-2,-7) the answer has to be in slope-intercept form y=?
Can anyone please help me with this?
Certainly! To find the equation of a line in slope-intercept form (y = mx + b), you need to first find the slope (m) and then the y-intercept (b).
The formula for the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Given the coordinates (-5, -9) and (-2, -7), we can substitute the values into the formula to find the slope:
m = (-7 - (-9)) / (-2 - (-5)) = (-7 + 9) / (-2 + 5) = 2 / 3
So, the slope (m) is 2/3.
Next, we can use one of the two given points and the slope to find the y-intercept (b). Let's use the point (-5, -9).
Using the slope-intercept form (y = mx + b), we can substitute the values of x and y from the point (-5, -9), and the slope (m = 2/3):
-9 = (2/3)(-5) + b
Now, we can solve for b:
-9 = (-10/3) + b
To isolate b, we can add 10/3 to both sides:
-9 + 10/3 = b
To simplify, we can find a common denominator for -9 and 10/3:
-27/3 + 10/3 = b
-17/3 = b
So, the y-intercept (b) is -17/3.
Now that we have the slope (m = 2/3) and the y-intercept (b = -17/3), we can write the equation of the line:
y = (2/3)x - 17/3
This is the equation of the line in slope-intercept form.