Hello Cristian,
Whenever the question asks for the equation of the line, it usually means it is asking for the slope intercept form (y = mx+b, where "m" is the slope and "b" is the y-intercept).
Step 1: Our first step should be do calculate the slope of the line "m". To determine slope, we use the equation (Y2-Y1)/(X2-X1)
Step 2. To calculate the slope, you subtract Y1 (which is 3 in this problem) from Y2 (which is 5 in this problem) and divide the difference with the difference of X1 (which is 1) from X2 (which is 8).
The setup for this problem should be: (5-3)/(8-1)
So after the differences in the numerator you get : 2/7
Which means that the slope of the line that goes through the points (1,3) and (8,5) is 2/7
Step 3: Plug the slope value in for "m" and you get: y = (2/7)x +b
Step 4: The next step is to determine the value of the y -intercept or "b". This can be done by plugging in one of the points already given. We will use (1,3) for this.
The setup for this problem will then be: 3 = (2/7)1 + b
Multiply the slope with the x-value to get 3 = (2/7) + b
Then subtract that product from both sides to get 3-(2/7) = b
To conduct the subtraction, there must be common denominators so multiply 3 by 7 in the numerator and the denominator to get : 21/7
Your resulting subtraction scenario will be: 21/7 -(2/7) = b
Now subtract to get 19/7 = b
Convert the new found value of "b" to a mixed fraction to get 2 and 5/7
Step 5: Plugin your "b" value to the equation to get the equation of the line to be: y = (2/7)x + 2 and (5/7)
Hope that helped!
