Question 103056
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

{{{(-4/5)/(8/5)}}}

Dividing by fractions can be handled by multiplying using the reciprocal, so:

{{{-(4/5)*(5/8)}}}

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).