Mathematics

Grade-8

Easy

Question

For x + $square root of 2$ y = 4,
Adam says x-intercept is 4
Sophia says y-intercept is 2 $square root of 2$
Elena says slope is $fraction numerator negative 1 over denominator square root of 2 end fraction$
Among them, whose answer is correct.

Adam and Sophia
Sophia and Elena
Elena and Adam
Adam, Sophia, and Elena

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 Adam, Sophia, and Elena.

The correct answer is: Adam, Sophia, and Elena

$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 x space plus square root of space 2 end root y space equals space 4 F o r space x minus i n t e r c e p t comma space y equals 0 x space plus square root of space 2 end root y space equals space 4 x space plus square root of space 2 end root open parentheses 0 close parentheses equals space 4 x space plus open parentheses 0 close parentheses space equals space 4 x space equals space 4 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 4 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 x space plus square root of space 2 end root y space equals space 4 0 space plus square root of space 2 end root y space equals space 4 square root of space 2 end root y space equals space 4 y space equals space fraction numerator 4 over denominator square root of 2 end fraction y space equals space 2 square root of 2 S o p h i a space s a y s space y minus i n t e r c e p t space i s space 2 square root of 2 space a n d space s h e space i s space c o r r e c t. 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 x space plus square root of space 2 end root y space equals space 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. x space plus square root of space 2 end root y space equals space 4 square root of 2 y space equals space 4 space minus space x y space equals space fraction numerator 4 space minus space x over denominator square root of 2 end fraction y space equals space open parentheses fraction numerator negative 1 over denominator square root of 2 end fraction close parentheses x space plus space fraction numerator 4 over denominator square root of 2 end fraction y space equals space space open parentheses fraction numerator negative 1 over denominator square root of 2 end fraction close parentheses x space plus space 2 square root of 2 y space equals space m x space plus thin space c H e r e comma space m space equals space space open parentheses fraction numerator negative 1 over denominator square root of 2 end fraction close parentheses E l e n a space s a y s space s l o p e space i s space space open parentheses fraction numerator negative 1 over denominator square root of 2 end fraction close parentheses space a n d space s 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 comma space S o p h i a comma space a n d space E l e n a.$

The sum of the intercepts of the equation 7x + 9y + 5 = 0 is

MathematicsGrade-8

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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

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The y-intercept of the line is $square root of 2$ and the slope is 4. The equation of line will be

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$text The end text y text -intercept of the equation end text square root of 5 plus square root of 4 x equals square root of 3 y text is end text$

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The equation of line with x-intercept 1 and y-intercept 0.1 is

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The x-intercept of the equation, “Taxi company charges $5 for booking and $0.2 for every km. Represent the equation, taking x as the number of km and y as the total amount” is

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.

The x-intercept of the equation, “Taxi company charges $5 for booking and $0.2 for every km. Represent the equation, taking x as the number of km and y as the total amount” is

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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.

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The x-intercept of the equation 2y + 3 = 2x is

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The difference between x and y-intercepts is

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x-intercept is same as the y-intercept and sum of the intercepts is 2. The equation of line will be

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x-intercept is twice of y-intercept and the sum of the intercepts is 6. The equation of line will be

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$text The end text y text -intercept of the equation end text square root of 2 x plus fraction numerator 5 over denominator square root of 2 end fraction equals square root of 3 y text is end text$

MathematicsGrade-8

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For x + y = 4,Adam says x-intercept is 4Sophia says y-intercept is 2Elena says slope is Among them, whose answer is correct.

Adam and SophiaSophia and ElenaElena and AdamAdam, Sophia, and Elena

The correct answer is: Adam, Sophia, and Elena

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For x + $square root of 2$ y = 4,
Adam says x-intercept is 4
Sophia says y-intercept is 2 $square root of 2$
Elena says slope is $fraction numerator negative 1 over denominator square root of 2 end fraction$
Among them, whose answer is correct.

Adam and Sophia
Sophia and Elena
Elena and Adam
Adam, Sophia, and Elena

The y-intercept of the line is $square root of 2$ and the slope is 4. The equation of line will be

The y-intercept of the line is $square root of 2$ and the slope is 4. The equation of line will be