Question

Consider the three points (-7, -7), (21, 14), (49, 35)

Answer 1

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:

$m = \frac{y_2-y_1}{x_2-x_1}$

Find the slope using (-7, -7) and (21, 14), we have :

$m = \frac{14 - - 7}{21 - - 7} = \frac{21}{28} = \frac{3}{4}$

The equation of this line through (-7, -7) and (21, 14),is given by

$y-y_1=m(x-x_1)$

We substitute the point and slope to get:

$y - - 7 = \frac{3}{4} (x - - 7)$

This gives us

$y = \frac{3}{4} x - \frac{7}{4}$

We check and see if the point (49,35) lies on the same line.

When x=49 do we get y=35?

$y = \frac{3}{4} \times 49 - \frac{7}{4} = \frac{147 - 7}{4} = \frac{140}{4} = 35$

Yes

For point A (5,9)

When x=5, do we get y=9?

$y = \frac{3}{4} \times 5 - \frac{7}{4} = \frac{15 - 7}{4} = \frac{8}{4} = 2 \ne9$

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?

$y = \frac{3}{4} \times 17 - \frac{7}{4} = \frac{51 - 7}{4} = \frac{46}{4} \ne11$

No

For point D (4,3)

When x=4, does y=3?

$y = \frac{3}{4} \times 4 - \frac{7}{4} = \frac{12 - 7}{4} = \frac{5}{4} \ne \: 3$

No

For point E (33,23)

When x=33, does y=23?

$y = \frac{3}{4} \times 33 - \frac{7}{4} = \frac{99 - 7}{4} = \frac{92}{4} = 23$

Yes