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Mathematics

Grade-8

Easy

Question

The graph of a linear function y = mx + b includes the points (3, 5) and (9, 5). Which of the following gives the correct values of m and b?

m = 5 and b = 7
m = 1 and b = 0
m = 0 and b = 5
m = 3 and b = 9

The correct answer is: m = 0 and b = 5

$y space equals space m x space plus space b space space space left parenthesis g i v e n space right parenthesis i t space i n c l u d e space t h e space p o i n t space left parenthesis space 3 comma 5 right parenthesis space a n d space left parenthesis 9 comma 5 right parenthesis comma space s o space b o t h space p o i n t s space s a t i s f y space t h e space g i v e n space e q u a t i o n y space equals space m x space plus space b 5 space equals space 3 m space plus space b..... left parenthesis a right parenthesis 5 space equals space 9 m space plus space b space..... left parenthesis b right parenthesis s u b s t r a c t space e q u a t i o n space a space a n d space b 0 space equals space minus 6 m space plus space 0 s o space m equals 0 p u t space t h e space v a l u e space o f space m space i n space e q u a t i o n space a space o r space b space w e space g e t space t h e space v a l u e space o f space b 5 space equals space 3 space x space 0 space plus space b s o space b space equals space 5 m equals 0 space a n d space b space equals space 5 space i s space t h e space c o r r e c t space a n s w e r$

second method
m = $fraction numerator left parenthesis 5 minus 5 right parenthesis over denominator left parenthesis 9 minus 3 right parenthesis end fraction$ = $fraction numerator 0 over denominator 6 end fraction$ =0
y = mx + b
5 = 0 + b
5 = b

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