Which of the following is an equation of the line in the xy plane with x-intercept −72 and y intercept 78 ?Choose 1 answer:(A) 7y−28x=8(B) 7y+28x=8(C) −7y+28x=8(D) −7y−28x=8
Q. Which of the following is an equation of the line in the xy plane with x-intercept −72 and y intercept 78 ?Choose 1 answer:(A) 7y−28x=8(B) 7y+28x=8(C) −7y+28x=8(D) −7y−28x=8
Intercept form of line equation: To find the equation of the line, we can use the intercept form of a line's equation, which is ax+by=1, where a is the x-intercept and b is the y-intercept.
Substituting x-intercept and y-intercept: Given the x-intercept is −72 and the y-intercept is 78, we substitute these values into the intercept form equation: −(72)x+(78)y=1.
Clearing the fractions: To clear the fractions, we multiply every term by the least common denominator, which in this case is 7: 7×(−(72)x)+7×(78y)=7×1.
Simplifying the equation: Simplifying the equation, we get −7×(−(72)x)+7×(78y)=7, which simplifies to −27x+87y=7.
Multiplying to clear fractions: Multiplying through by the denominators to clear the fractions gives us (7x×(−27))+(7y×(87))=7×7.
Getting rid of fractions: Simplifying the equation, we get −249×x+849×y=49.
Multiplying to simplify: To get rid of the fractions, we can multiply the entire equation by the least common multiple of the denominators, which is 8: 8×(−249×x)+8×(849×y)=8×49.
Dividing to simplify: Simplifying the equation, we get −4×49×x+49×y=8×49.
Rearranging to standard form: This simplifies to −196x+49y=392.
Matching the answer choices: Dividing the entire equation by 49 to simplify it further, we get −4x+y=8.
Checking our work: Finally, we rearrange the equation to match the standard form Ax+By=C, which gives us y+4x=8.
Checking our work: Finally, we rearrange the equation to match the standard form Ax+By=C, which gives us y+4x=8. Multiplying the entire equation by 7 to match the answer choices, we get 7y+28x=56.
Checking our work: Finally, we rearrange the equation to match the standard form Ax+By=C, which gives us y+4x=8. Multiplying the entire equation by 7 to match the answer choices, we get 7y+28x=56. We notice that none of the answer choices match the equation 7y+28x=56. We must have made a mistake in our calculations. Let's go back and check our work.
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