Answer:
b , c and e
Step-by-step explanation:
The first step is to find the slope of the given line
Calculate the slope m, using the slope formula
• m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
let (x₁, y₁ ) = (- 2, - 4) and (x₂, y₂ ) = (4, 2) ← 2 points on the line
substitute these values into the formula for m
m = [tex]\frac{2-(-4)}{4-(-2)}[/tex] = [tex]\frac{2+4}{4+2}[/tex] = [tex]\frac{6}{6}[/tex] = 1
• Parallel lines have equal slopes
The equation of a line in slope- intercept form is
• y = mx + c ( m is the slope and c the y- intercept (
the line passes through the y- axis at P (0, 4 ) , then c = 4
y = x + 4 ← equation of line through P
To determine which points lie on this line
substitute the x- coordinate into the right side of the equation and if the value obtained is equal to the y- coordinate of the point, then it lies on the line.
(a) (- 4, 2 )
y = - 4 + 4 = 0 ≠ 2 ← not on line
(b) (- 1, 3 )
y = - 1 + 4 = 3 ← lies on line
(c) (- 2, 2 )
y = - 2 + 4 = 2 ← lies on line
(d) (4, 2 )
y = 4 + 4 = 8 ≠ 2 ← not on line
(e) (- 5, - 1 )
y = - 5 + 4 = - 1 ← lies on line
The 3 points which lie on the line through P are (b) , (c ) and (e )
