Answer/Step-by-step explanation:
✍️Slope of the line using two points, (2, 2) and (6, 10),
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 2}{6 - 2} = \frac{8}{4} = 2 [/tex]
✍️To find the equation of the line in slope-intercept form, we need to find the y-intercept (b).
Substitute x = 2, y = 2, and m = 2 in y = mx + b, and solve for b.
2 = (2)(2) + b
2 = 4 + b
2 - 4 = b
-2 = b
b = -2
Substitute m = 2 and b = -2 in y = mx + b.
✅The equation would be:
[tex] y = 2x + (-2) [/tex]
[tex] y = 2x - 2 [/tex]
✍️To find the value of a, plug in (a, 8) as (x, y) into the equation of the line.
[tex] 8 = 2(a) - 2 [/tex]
[tex] 8 = 2a - 2 [/tex]
Add 2 to both sides
[tex] 8 + 2 = 2a [/tex]
[tex] 10 = 2a [/tex]
Divide both sides by 2
[tex] \frac{10}{2} = a [/tex]
[tex] 5 = a [/tex]
a = 5
✍️To find the value of b, plug in (4, b) as (x, y) into the equation of the line.
[tex] b = 2(4) - 2 [/tex]
[tex] b = 8 - 2 [/tex]
[tex] b = 6 [/tex]
