1.05 Algebra Ii Essay

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01.05 Writing the Equation of a Line Log the coordinates of the specific points in space to which your spacecraft will travel. Please remember to include the graph of your points and the lines connecting each point along with your work. Launch Area:___(1, 2)___ Point A: (1,4) Point B: (3,5) Point C: (5,3) You must show your work on each question below. 1.Determine the equation of the line, in standard form, that will get your spacecraft from the Launch Area to Point A. ax+by=c 1x+0y=1 x=1 2. Determine the equation of the line, in point-slope form, that will get your spacecraft from Point A to Point B. y-y1=m(x-x1) (x1,y1)=(1,4) m=y2-y1/x2-x1 (x2,y2)=(3,5) m=5-4/3-1 m=1/2 y-4=1/2(x-1) 3. Determine the equation of the line, in slope-intercept form, that will get your spacecraft from Point B to Point C. y=mx+b 3=5m+b 5=3m+b b=b 3-5m=5-3m -2=2m -2/2=m -1=m 3=-1(5)+b 3=-5+b 5+3=b 8=b y=-1x+8 4. In question 2, you selected one of two points (Point A or Point B) to be included in your point-slope equation. Write the point-slope form of that equation again, using the other point’s coordinates. y-y1=m(x-x1) y-5=1/2(x-3) 5. Convert the equations you arrived at in question 2 and question 4 into slope-intercept form. 2: 2(y-4)=(x-1) 2y-8=x-1 2y-x=-1+8 2y=x+7 4: 2(y-5)=(x-3) 2y-10=x-3 2y=x-3+10 2y=x+7 6. Does the point you select matter when your write a point-slope equation? Explain your reasoning using complete sentences. No, because I could have chose any points, and still put them in point slope form. It would have worked the same, just with a different answer, and equation. 7.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. No, because a line is the set of all points. As long as the point

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