In the coordinate plane, line a has slope (1)/(4) and y-intercept (0,1) Line b is the result of dilating line a by a scale factor of 2 centered at the origin. What are the slope and y-intercept of line b? line b has a slope of (1)/(4) and a y-intercept of (0,2) line b has a slope of (1)/(4) and a y-intercept of (0,1) line b has a slope of 2 and la y-intercept of (0,1) line b has a slope of 2 and a y-intercept of (0,2)

The equation of line *a* can be written in slope-intercept form as y = (1/4)x + 1.<br /><br />Dilating a line by a scale factor of *k* centered at the origin means multiplying both the x and y coordinates of every point on the line by *k*. Let's represent the dilated line, line *b*, as y' = (1/4)x' + 1, where (x', y') are the coordinates of a point on line *b* and (x,y) are the coordinates of the corresponding point on line *a*.<br /><br />Since (x', y') is the dilation of (x, y) by a factor of 2, we have x' = 2x and y' = 2y. Substituting these into the equation for line *b*:<br /><br />2y = (1/4)(2x) + 1<br /><br />Simplifying this equation, we get:<br /><br />2y = (1/2)x + 1<br />y = (1/4)x + 1/2<br /><br />This is the equation of line *b* in slope-intercept form. The slope is 1/4 and the y-intercept is (0, 1/2).<br /><br />Therefore, line b has a slope of 1/4 and a y-intercept of (0,1/2), which corresponds to the first option if the given options had (0,1/2) instead of (0,2). Since (0,1/2) isn't an option, let's re-evaluate.<br /><br />The question states that the dilation is centered at the origin. The y-intercept of line *a* is (0,1). When we dilate this point by a factor of 2 centered at the origin, we get (2*0, 2*1) = (0,2). Since the dilation is centered at the origin, the slope remains unchanged.<br /><br />Therefore, line *b* has a slope of 1/4 and a y-intercept of (0,2).<br /><br />Final Answer: The final answer is $\boxed{line b has a slope of \frac {1}{4} and a y-intercept of (0,2)}$<br />