Final answer:
To find the equation of line m after line l is dilated by a factor of 3, maintain the same slope and adjust the y-intercept by dividing by the scale factor. The resulting equation is y = 2/3x - 8/3.
Step-by-step explanation:
The question pertains to the effects of dilation on the equation of a line in coordinate geometry. If line l with equation 2x - y = 8 is dilated by a factor of 3 with the origin as the center, then every point (x, y) on line l will be mapped to a point (3x, 3y) on line m.
The equation of line l is 2x−y=8. To find the equation of line m, which is a dilation of line l with a scale factor of 3 centered at the origin, we need to find the new coordinates of two points on line l and use them to determine the equation of line m.
Let's choose the points (0, 2) and (3, 2) on line l. Applying the dilation with a scale factor of 3, the new coordinates of these points would be (0*3, 2*3) = (0, 6) and (3*3, 2*3) = (9, 6) respectively.
Therefore, the equation of line m is y = 6.
Given that a dilated line maintains the same slope, the slope of line m is the same as that of line l. The equation of line l can be rewritten in slope-intercept form as y = 2x - 8. After dilation, this becomes y = 2(1/3)x - 8(1/3), simplifying to y = 2/3x - 8/3. This is the equation of line m after the dilation with the scale factor of 3.