Answer:
B
Step-by-step explanation:
• Parallel lines have equal slopes
calculate the slope m of the given line using the gradient formula and compare to the slope of the equations given
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (1,1) ← 2 points on the line
m = [tex]\frac{1+1}{1+1}[/tex] = 1 ← slope of graph
consider the slope of the given equations
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
(A)
y = 2x + 1 has slope = 2 → not parallel
(B)
x - y = - 3 ( subtract x from both sides )
- y = - x - 3 ( multiply through by - 1 )
y = x + 3 with slope = 1 → thus parallel to graph
(C)
x + y = 2 ( subtract x from both sides )
y = - x + 2 with slope = - 1 → not parallel
(D)
y = - x + 1 with slope = - 1 → not parallel
