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Mathematics

Grade-8

Easy

Question

For $square root of 2 x plus square root of 3 y equals square root of 4$ ,
Adam says x-intercept is $square root of 2$
Jack says y-intercept is $square root of 3$
John says slope is $fraction numerator negative square root of 2 over denominator square root of 3 end fraction$
The correct answers were given by

Adam and Jack
Jack and John
John and Adam
Adam, Jack, and John

hint Hint:

A y-intercept is a point where the graph of a function or relation intersects with the y-axis of the coordinate system. To find the y-intercept, set x = 0 and solve for y.
An x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system. To find the x-intercept set y = 0 and solve for x.
In the standard equation of a line, y = mx + b, the slope is m. It is also commonly described as "rise over run" which tells us how much the y-value changes as the x-value changes.
Solve for all the three terms and compare with the statements given by John, Jack and Adam.

The correct answer is: John and Adam

$T o space f i n d space o u t space w h o space i s space c o r r e c t comma space w e space n e e d space t o space f i n d space t h e space x space a n d space y minus i n t e r c e p t s space a n d space t h e space s l o p e space o f space t h e space g i v e n space l i n e. T h e space e q u a t i o n space o f space t h e space l i n e space i s space square root of 2 x space plus space square root of 3 y space equals space square root of 4 F o r space x minus i n t e r c e p t comma space y equals 0 square root of 2 x space plus space square root of 3 y space equals space square root of 4 square root of 2 x space plus space square root of 3 open parentheses 0 close parentheses space equals space square root of 4 square root of 2 x space plus space 0 space equals space square root of 4 x space equals space fraction numerator square root of 4 over denominator square root of 2 end fraction x space equals space square root of 2 A d a m space s a y s space x minus i n t e r c e p t space i s space square root of 2 space w h i c h space i s space c o r r e c t. F o r space y minus i n t e r c e p t comma space x equals 0 square root of 2 x space plus space square root of 3 y space equals space square root of 4 square root of 2 open parentheses 0 close parentheses space plus space square root of 3 y space equals space square root of 4 0 space plus space square root of 3 y space equals space square root of 4 y space equals space fraction numerator square root of 4 over denominator square root of 3 end fraction y space equals space fraction numerator 2 over denominator square root of 3 end fraction J a c k space s a y s space y minus i n t e r c e p t space i s space square root of 3 space b u t space i t space i s space fraction numerator 2 over denominator square root of 3 end fraction comma space t h e r e f o r e comma space h e space i s space w r o n g. T o space f i n d space t h e space s l o p e comma t h e space g i v e n space e q u a t i o n space i s square root of 2 x space plus space square root of 3 y space equals space square root of 4 L e t apostrophe s space c o n v e r t space i t space i n t o space t h e space s l o p e space e q u a t i o n space t o space c o m p a r e space i t space w i t h space y equals m x plus c. square root of 3 y space equals space square root of 4 space minus space square root of 2 x y space equals space fraction numerator square root of 4 space minus space square root of 2 x over denominator square root of 3 end fraction y space equals negative space open parentheses fraction numerator square root of 2 over denominator square root of 3 end fraction close parentheses x space plus space open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses y space equals space m x space plus thin space c H e r e comma space m space equals space minus space fraction numerator square root of 2 over denominator square root of 3 end fraction J o h n space s a y s space s l o p e space i s space minus space fraction numerator square root of 2 over denominator square root of 3 end fraction space a n d space h e space i s space c o r r e c t T h e r e f o r e comma space t h e space c o r r e c t space a n s w e r s space w e r e space g i v e n space b y space A d a m space a n d space J o h n.$

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