Algebra 2 Essay

Launch Area:___(1, 2)___
Point A:___(0, 3)___
Point B:___(-3, 0)___
Point C:___(-1, -4)___
1. Graph the coordinates of the specifics points in space your spacecraft will travel to.
You must show your work on each question below.
2. Determine the equation of the line, in standard form, that will get your spacecraft from the Launch Area to Point A.
3. Determine the equation of the line, in point-slope form, that will get your spacecraft from Point A to Point B.
4. Determine the equation of the line, in slope-intercept form, that will get your spacecraft from Point B to Point C.
5. Convert the equations you arrived at in question 2 and into slope-intercept form. Make sure to include all of your work.
6. Reflect back on this scenario and each equation you created. Would any restrictions apply to the domain and range of those equations? Explain your reasoning using complete sentences.

Answers:

1.)

2.) First, let’s find the slope from Launch Area to point A. m=y2-y1/x2-x1, m=2-3/1-0. This equals -1/1 or just -1. Now we can use point-slope form (y-y1) =m(x-x1).I will now use point A, (0,3) so it would look like this: y-(3)=-1(x-0)=(y-3=-1x+0)=(1x+y-3=0)=(x+y=3)So in standard form, the equation would be x+y=3.
3.) First, let’s find the slope from point A to point B. m=0-3/-3-0. This equals -3/-3, which reduces to positive 1. Now, we can use point-slope form. I will use point B and it would look like this: y-(0)=1(x-(-3)). So once it’s simplified in point-slope form, it would look like this: y-0=1(x+3).
4.) First, let’s find the slope from point B to point C. m=-4-0/-1-(-3). This equals -4/2, which reduces to -2. Now, we can use point-slope form and then rearrange it to make it into slope-intercept form. Since I’m using point C, it should look like this: y-(-4)=-2(x+1)=(y+4=-2x-2)=(y=-2x-6). So the answer in