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Given: AB || CD. If the coordinates of point A are (8, 0) and the coordinates of point B are (3, 7), what is the Y-intercept of line AB? The coordinates of point D are (5, 5), what is the equation of line CD?

a) Y-intercept of AB = 4; Equation of CD: y = x
b) Y-intercept of AB = 7; Equation of CD: y = x + 2
c) Y-intercept of AB = 5; Equation of CD: y = x - 2
d) Y-intercept of AB = 0; Equation of CD: y = x - 2

User Alex Sed
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1 Answer

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Final answer:

The y-intercept of line AB is 0. The equation of line CD is y = -x + 10.

Step-by-step explanation:

The y-intercept of line AB can be found using the formula for the equation of a line, which is in the form y = mx + b. In this case, we need to find the value of b, which represents the y-intercept. To find b, we can substitute the coordinates of point A, (8, 0), into the equation and solve for b. When we substitute the values, we get 0 = 8m + b. Since the line AB is parallel to the y-axis, the slope, m, is undefined. Therefore, the equation reduces to 0 = b. So, the y-intercept of line AB is 0.

The equation of line CD can be found using the coordinates of points C and D. We can use the slope-intercept form of the equation, y = mx + b, where m is the slope and b is the y-intercept. The slope of CD can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of points C and D, respectively. Substituting the values from the coordinates, we get m = (5 - 7) / (5 - 3) = -2 / 2 = -1. So, the slope of CD is -1. Using this slope and the coordinates of point D, we can substitute them into the equation y = mx + b and solve for b. Substituting the values, we get 5 = -5 + b. Solving for b, we find that b = 10. Therefore, the equation of line CD is y = -x + 10.

User Greg Hornby
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