Which of the following is an equation of the line in the xy-plane that passes through the point (1,1) and is parallel to the line with equation y=-3x-1 ? Choose 1 answer: A) y=(1)/(3)x+4 (B) y=(1)/(3)x+1 (c) y=-3x+4 (D) y=-3x+1

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Which of the following is an equation of the line in the  xy-plane that passes through the point  (1,1) and is parallel to the line with equation  y=-3x-1 ? Choose 1 answer: A)  y=(1)/(3)x+4 (B)  y=(1)/(3)x+1 (c)  y=-3x+4 (D)  y=-3x+1

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Identify slope of given line: The question prompt is: ＂What is the equation of the line that passes through the point (1,1) and is parallel to the line with equation y = -3x - 1?＂Determine slope of parallel line: Identify the slope of the given line. The equation of the given line is y = -3x - 1, which is in slope-intercept form y = mx + b, where m is the slope. The slope of the given line is -3.Use point-slope form to find equation: Determine the slope of the line that is parallel to the given line. Lines that are parallel have the same slope. Therefore, the slope of the line we are looking for is also -3.Simplify equation to slope-intercept form: Use the point-slope form of the equation of a line to find the equation of the line that passes through the point (1,1) with the slope -3. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substitute (1,1) for (x1, y1) and -3 for m. y - 1 = -3(x - 1)Compare equation with answer choices: Simplify the equation to get it into slope-intercept form y = mx + b. y - 1 = -3x + 3 Add 1 to both sides to isolate y. y = -3x + 3 + 1 y = -3x + 4Compare the equation y = -3x + 4 with the answer choices. The correct answer choice will have the same slope -3 and y-intercept 4. The correct answer is (C) y = -3x + 4.

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