Question 1093523: What is the equation of the line that passes through the points (-1,1) and (4,7)?
Found 2 solutions by Yanira_Sierra, greenestamps:
Answer by Yanira_Sierra(1)   (Show Source):
You can put this solution on YOUR website! Find the slope:
(-1,1) - stays the same
(-4,-7) - change the signs. -subtracting x values and y values
-5 , -6 add the numbers vertically. m(slope)= rise / run = -6/-5 = 6/5
Choose a point from the original problem. (4,7). x=4 y=7 and m= 6/5
Substitute all three values into the equation: y=mx+b. Then solve for b.
y = m x + b
7 =(6/5)(4) + b multiply the 6 and 4
7 = 24/5 + b you get 24. Now multiply everything by 5.
35 = 24 + b The fraction canceled.
11 = b Subtract 24 on both sides
Last Step: Substitute b = 11 and m = 6/5 back into the equation : y = m x + b
y = 6/5 x + 11
Yay!!! We now know that the points (-1,1) and (4,7) pass through the line y = 6/5 x + 11.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
While most of the work in the first response you got was okay, I had a hard time following it because of the language she used. And there is an error near the end which leads to an incorrect final answer.
I encourage you to understand what slope means, rather than blindly plugging numbers into the "m equals y2-y1 divided by x2-x1" formula. The slope is a measure of how fast you go up or down as you move to the right on the graph. Think of the line as a path you are hiking along; the slope is how fast you get higher or lower as you walk forward.
So to find the slope, look at the numbers to see that you are moving from -1 to 4 in the x ("forward") direction, a distance of 5. In doing that, the y value changes from 1 to 7, an increase of 6. So in walking forward 5 steps, you climbed up 6 steps. Since slope is a measure of how fast you go up or down compared to how far you move forward, the slope is 6/5.
Now one form of the equation of a line is y=mx+b, where m is the slope. We have determined that the slope is 6; we can use the x and y values of one of the points that we know are on the line to determine the value of b and thus complete the equation of the line. Using the point (x,y) = (-1,1),
Now we know both the slope m and the y-intercept b, so we can write the whole equation:
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