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Maths-

SAT

Easy

Question

A line is shown in the xy-plane above. A second line (not shown) is parallel to the line shown and passes through the points (1, 1) and (3, c), where c is a constant. What is the value of c ?

The correct answer is: 2.5

The given line passes through (4,- 2 ) & (0,-5)
Slope of parallel lines is equal
$m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator negative 5 plus 2 over denominator 0 minus 4 end fraction equals fraction numerator negative 3 over denominator negative 4 end fraction equals 3 over 4$
The required line is y = mx + b
$y equals 3 over 4 x plus b$ passes through (1,1)
$1 equals 3 over 4 x plus b$
$1 fourth equals b$
$y equals 3 over 4 x plus 1 fourth$
4y = 3x + 1 passes through (3, c)
4c = 3(3) + 1
4c = 10
$c equals 10 over 4 equals 2.5$

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