Final answer:
The dilation of the line y = 7x - 4 by a scale factor of 5/2 and centred at the origin will affect the y-intercept but maintain the slope. Thus, the statement as given is False because it does not clarify the necessary change in the y-intercept due to dilation.
Step-by-step explanation:
The question addresses the concept of dilation in the context of coordinate geometry, which is a transformation that changes the size (but not the shape) of a figure by a given scale factor. A line represented by an equation y = mx + b, when dilated by a scale factor and centred at the origin, will have every point on the line move radially away from the origin by that scale factor. So, for a line y = 7x - 4, if we apply a dilation centred at the origin with a scale factor of 5/2, the slope remains the same, but the y-intercept will be scaled by the same factor.
Therefore, by multiplying the y-intercept by 5/2, the new line's equation will be y = 7x - (4 * 5/2). We can conclude that the original statement lacks sufficient information or is misleading, as it does not provide a new equation nor mentions maintaining the slope.
So, based on the provided information, the statement seems to be False because it doesn't fully explain the transformation that occurs to the y-intercept after dilation.