Answer:
z=2
Step-by-step explanation:
We are given that a line has a slope of 3.
The line passes through the points (-10, z) and (-8, 8)
We want to find the value of z.
To do that, we can calculate the slope.
The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
Even though we already have 2 points, let's label their values to avoid any confusion.
[tex]x_1=-10\\y_1=z\\x_2=-8\\y_2=8[/tex]
Now substitute those values into the formula, and set it equal to 3. Remember that the formula uses subtraction.
[tex]\frac{8-z}{-8--10}[/tex] = 3
We can simplify this first.
[tex]\frac{8-z}{-8+10}[/tex] = 3
[tex]\frac{8-z}{2}[/tex] = 3
We can multiply both sides by 2 to clear the fraction and make it easier to calculate.
2([tex]\frac{8-z}{2}[/tex]) = 2(3)
Multiply.
8 - z = 6
Subtract 8 from both sides
-z = - 2
Multiply both sides by -1.
-1(-z) = -1(-2)
Multiply.
z = 2
