In the xy -plane, line k intersects the y -axis at the point and passes through the point . If

Question

In the xy -plane, line k intersects the y -axis at the point and passes through the point . If the point lies on line k , what is the value of w ?

Accepted Answer

The correct answer is 74. The y -intercept of a line in the xy -plane is the ordered pair of the point of intersection of the line with the y -axis. Since line k intersects the y -axis at the point , it follows that is the y -intercept of this line. An equation of any line in the xy -plane can be written in the form , where m is the slope of the line and b is the y -coordinate of the y -intercept. Therefore, the equation of line k can be written as , or . The value of m can be found by substituting the x - and y -coordinates from a point on the line, such as , for x and y, respectively. This results in . Solving this equation for m gives . Therefore, an equation of line k is . The value of w can be found by substituting the x -coordinate, 20, for x in the equation of line k and solving this equation for y. This gives , or . Since w is the y -coordinate of this point, .

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