Answer:
To find the slope and y-intercept of line n, which is the result of dilating line m by a scale factor of 4 with a center of (0,0), we need to consider the properties of dilation.
When a line is dilated by a scale factor of k, the slope of the dilated line remains the same as the original line, while the y-intercept is multiplied by the scale factor.
Given that line m has a slope of 2 and a y-intercept of (0, -5), the slope of line n will also be 2, as dilation does not change the slope.
For the y-intercept of line n, we multiply the y-intercept of line m (-5) by the scale factor of 4:
y-intercept of line n = scale factor * y-intercept of line m
= 4 * (-5)
= -20
Therefore, line n has a slope of 2 and a y-intercept of (0, -20).
Among the given answer choices, the correct option is:
c. Line n has a slope of 2 and a y-intercept of (0, -20).