It's easiest to start with the point-slope form of an equation,
, where m is the slope and
is the point given.
We have m = 3,
, and
.
We plug in these values to get
.
We now rearrange to get this into slope-intercept form,
, by solving for y.
Let A, M, and w represent Angelo's distance per week, Marc's distance per week, and the number of weeks of this regimen, respectively.
.. A = w +7 . . . . . . . Angelo's distance goes up 1 mile/week each week
.. M = 2w +4 . . . . . Marc's distance goes up 2 miles/week each week
a) A = M
.. w +7 = 2w +4
.. 3 = w . . . . . . . . . . subtract w+4
After 3 weeks Angelo and Marc will be running the same distance.
b) A = M = 3+7 = 2*3+4 = 10
That distance will be 10 miles per week.
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This problem can be a little confusing because "miles per week" is a rate, and we're talking about the rate of increase of that rate: 1 or 2 miles per week per week. It might be easier to think of the numbers as "weekly distance", rather than "miles per week".
That is not possible to make a triangle with a right angle and a acute angle because a acute triangle only has acute angles and a right triangle has a obtuse angle in it
