Answer:
z = 3
Step-by-step explanation:
Since the points are collinear then the slopes between the points are equal.
Calculate the slope m using the slope formula
m =
with (x₁, y₁ ) = P (2, - 3) and (x₂, y₂ ) = Q (3, - 2)
m = = 1
Repeat with
(x₁, y₁ ) = Q (3, - 2) and (x₂, y₂ ) = R (8, z )
m = =
, then
= 1 ( multiply both sides by 5 )
z + 2 = 5 ( subtract 2 from both sides )
z = 3
<em>(Solving for x on question - 2x + 3y = 32)</em>
2x + 3y = 32
Step 1: Add -3y to both sides.
2x + 3y + −3y = 32 + −3y
2x = −3y + 32
Step 2: Divide both sides by 2.
=
<u>x = </u><u>⁻y + 16</u><u> </u>
<em>(Solving for y on question - 2x + 3y = 32)</em>
2x + 3y = 32
Step 1: Add -2x to both sides.
2x + 3y + −2x = 32+ −2x
3y = −2x + 32
Step 2: Divide both sides by 3.
=
<u>y = </u><u>x + </u>
<u> </u>
<em>(Solving for x on question - 5x - 4y = -81)</em>
5x − 4y = −81
Step 1: Add 4y to both sides.
5x − 4y + 4y = −81 + 4y
5x = 4y − 81
Step 2: Divide both sides by 5.
=
<u>x = </u><u>y + </u>
<u> </u>
<em>(Solving for y on question - 5x - 4y = -81 )</em>
5x − 4y = −81
Step 1: Add -5x to both sides.
5x − 4y + −5x = −81 + −5x
−4y = −5x − 81
Step 2: Divide both sides by -4.
=
y = x +