Answer:
z = 3
Explanation:
First we want to find out how they found the slope of the line. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(6 - 0)/ (4 - z)
Simplify the parentheses.
= (6) / (4 - z)
Simplify the fraction.
= 6/(4 - z)
it is given that 6 is your slope. So let's add 6 to the left side of the equal sign.
6 = 6 / (4 - z)
To solve for z, we need to multiply both sides by (4 - z)
(4 - z)6 = 6
Now, divide both sides by 6 to isolate the expression of (4 - z)
4 - z = 1
Add z to both sides so it becomes positive.
4 = z + 1
Subtract 1 from both sides to isolate z.
3 = z
This is your answer.
Let's check it by plugging it back into the slope formula.
(6 - 0)/ (4 - z)
(6 - 0)/ (4 - 3)
= 6/1
= 6
Your answer is correct.
Hope this helps!