Answer:
b = 0
Step-by-step explanation:
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - 2x + 17 is in this form with slope m = - 2
• Parallel lines have equal slopes, hence
slope of line through the 2 points is - 2
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (b, 7)
m = [tex]\frac{7-3}{b-2}[/tex] = [tex]\frac{4}{b-2}[/tex], hence
[tex]\frac{4}{b-2}[/tex] = - 2 ( cross- multiply )
- 2(b - 2) = 4
- 2b + 4 = 4 ( subtract 4 from both sides )
- 2b = 0 ⇒ b = 0
