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The equation of line r is y = -x - 6. Line s includes the point (1, 3) and is parallel to line r. What is the equation of line s? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions, improper fractions, or integers.

a) y = -x + 4
b) y = -x + 3
c) y = -x + 2
d) y = -x + 6

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Final answer:

Line s, parallel to line r (y = -x - 6), and passing through (1, 3), has the same slope as r, which is -1. Substituting values into the equation y = mx + b, we calculate the y-intercept to be 4. Thus, the equation of line s is y = -x + 4.

Step-by-step explanation:

The question asks for the equation of a line s that is parallel to line r, where the equation of line r is given as y = -x - 6 and line s must pass through the point (1, 3). Since lines that are parallel have the same slope, the slope of line s will also be -1, as that is the slope of line r. To find the y-intercept of line s, we use the point that it passes through. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b is the y-intercept. Substituting the slope (-1) and the point (1, 3) into the slope-intercept form, we get the equation y = -1x + b. Plugging in the point gives us 3 = (-1)(1) + b, which simplifies to b = 3 + 1 = 4. Therefore, the equation of line s in slope-intercept form is y = -x + 4.

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