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rosijanka [135]
3 years ago
12

A line that passes through th epoints (2,3) and (b,7) is parallel to the line y = -2x + 17. Find the value of b

Mathematics
1 answer:
mel-nik [20]3 years ago
4 0

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 = \frac{7-3}{b-2} = \frac{4}{b-2}, hence

\frac{4}{b-2} = - 2 ( cross- multiply )

- 2(b - 2) = 4

- 2b + 4 = 4 ( subtract 4 from both sides )

- 2b = 0 ⇒ b = 0



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