Answer:
2nd, 3rd and 5 th
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = [tex]\frac{2}{3}[/tex] and (a, b) = (1, 2) , thus
y - 2 = [tex]\frac{2}{3}[/tex] (x - 1) ← 2 nd option
Using (a, b) = (4, 4), then
y - 4 = [tex]\frac{2}{3}[/tex] (x - 4) ← 3 rd option
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{2}{3}[/tex] , thus
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (4, 4) into the partial equation
4 = [tex]\frac{8}{3}[/tex] + c ⇒ c = 4 - [tex]\frac{8}{3}[/tex] = [tex]\frac{4}{3}[/tex]
f(x) = [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← 5 th option
