Answer:
1. Slope= 2
2. [tex] \frac{b - 2}{4 - 2} = 2[/tex] or [tex] \frac{8 - 2}{a - 2} = 2[/tex]
3. a= 5
4. b= 6
Step-by-step explanation:
The slope of a straight line between any two points of the line would be the same. This means that calculating the slope of the line using point (2, 2) and (6, 10) would give us the same slope value when calculating with points (4, b) and (6, 10) for example.
Formula
[tex]\boxed{\text{slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Q1. Since we two pairs of known coordinates, let's make use of them in the slope calculation.
Slope of line
[tex] = \frac{10 - 2}{6 - 2} [/tex]
[tex] = \frac{8}{4} [/tex]
= 2
Q2-4. Since in the subsequent parts we will eventually have to find the value of a and b, let's form an equation for each of them.
Slope between (2, 2) and (4, b)= slope between (2, 2) and (6, 10)
[tex] \frac{b - 2}{4 - 2} = 2[/tex]
[tex] \frac{b - 2}{2} = 2[/tex]
Multiply both sides by 2:
b -2= 2(2)
b -2= 4
b= 4 +2
b= 6
Using (2, 2) and (a, 8):
[tex] \frac{8 - 2}{a - 2} = 2[/tex]
Multiply both sides by (a -2):
6= 2(a -2)
Expand:
6= 2a -4
Add 4 to both sides:
2a= 10
Divide both sides by 2:
a= 10 ÷2
a= 5
To learn more about slope, check out: https://brainly.com/question/14548961
