Question 103056This question is from textbook
: I do not understand this question - please help me
Find the slope of the line through the given points. Also find the slope intercept form. Find the Y intercept and the X intercept for one of the points.
(-7/5, 3/10) and 1/5, -1/2)
This question is from textbook
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The two points are (-7/5, 3/10) and (1/5, -1/2).
The slope is the rise / run = change in y divided by the change in x.
Change in y = -1/2 - 3/10 = -5/10 - 3/10 = -8/10 = -4/5.
Change in x = 1/5 - (-7/5) = 1/5 + 7/5 = 8/5.
So the slope is
Dividing by fractions can be handled by multiplying using the reciprocal, so:
The 5's cancel each other, so you have slope = -4/8 = -1/2.
By convention, we call that m. It fits into the standard equation for a line, which you may recall is y = mx + b.
So, we now know that y = -1/2x + b.
But what is b?
That is the place the line crosses the y-axis when when x=0, or the y-intercept. But that is just a definition, not an answer.
Hmmm....
Well, we know one of the points is (1/5, -1/2), so that is a valid (x,y) pair.
Substituting what we know into y = mx + b, we have:
-1/2 = -1/2*1/5 + b
Multiplying:
-1/2 = -1/10 + b
Now add 1/10 to both sides:
-1/2 + 1/10 = b
-5/10 + 1/10 = b
-4/10 = b = -2/5
Aha!
y = -1/2x - 2/5.
Looking back at the question, it also calls for us to find the x-intercept. That is the place it crosses the x-axis when y=0.
So, substituting y=0:
0 = -1/2x - 2/5
Adding 2/5 to both sides:
2/5 = -1/2x
Multiplying by 2 to eliminate the fractional coefficient of x:
4/5 = -x
Multiplying by -1 to get x to be positive:
x = -4/5.
So, the x-intercept is at x=-4/5 (that is, the pair (-4/5,0).
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