Answer:
Part a) B (5,2) and E (33,23) lie on the line
A (5,9) ,C. (17, 11) and D. (4,3) do not lie on the line.
Part b) By substituting the given point into the equation of the line going through (-7, -7), (21,14), (49, 35).
Step-by-step explanation:
Given the three points (-7, -7), (21,14), (49, 35);
We find the slope using:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Find the slope using (-7, -7) and (21, 14), we have :
[tex]m = \frac{14 - - 7}{21 - - 7} = \frac{21}{28} = \frac{3}{4} [/tex]
The equation of this line through (-7, -7) and (21, 14),is given by
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and slope to get:
[tex]y - - 7 = \frac{3}{4} (x - - 7)[/tex]
This gives us
[tex]y = \frac{3}{4} x - \frac{7}{4} [/tex]
We check and see if the point (49,35) lies on the same line.
When x=49 do we get y=35?
[tex]y = \frac{3}{4} \times 49 - \frac{7}{4} = \frac{147 - 7}{4} = \frac{140}{4} = 35[/tex]
Yes
For point A (5,9)
When x=5, do we get y=9?
[tex]y = \frac{3}{4} \times 5 - \frac{7}{4} = \frac{15 - 7}{4} = \frac{8}{4} = 2 \ne9[/tex]
No
For point B (5,2)
When x=5, do we get y=2?
Yes, that's what we just got in A above.
For point C (17,11)
When x=17, do we get y=11?
[tex]y = \frac{3}{4} \times 17 - \frac{7}{4} = \frac{51 - 7}{4} = \frac{46}{4} \ne11[/tex]
No
For point D (4,3)
When x=4, does y=3?
[tex]y = \frac{3}{4} \times 4 - \frac{7}{4} = \frac{12 - 7}{4} = \frac{5}{4} \ne \: 3[/tex]
No
For point E (33,23)
When x=33, does y=23?
[tex]y = \frac{3}{4} \times 33 - \frac{7}{4} = \frac{99 - 7}{4} = \frac{92}{4} = 23[/tex]
Yes