In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests,
1 answer:
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Answer:
Answer 1.
Step-by-step explanation:
The complete question is:
The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 3 centered at the origin. Which statement is correct?
1. The image of the line has the same slope as the pre-image but a different y-intercept.
2. The image of the line has the same y-intercept as the pre-image but a different slope.
3. The image of the line has the same slope and the same y-intercept as the pre-image.
4. The image of the line has a different slope and a different y-intercept from the pre-image.
Recall that a dilation by a scale factor r centered at the origin takes a point (x,y) and maps it to the point (r*x,r*y).
Consider also a line of equation . From this equation, the slope of the line is given by the number
and the y-intercept is given by
.
Consider the given equation 3x-5y =4. If we replace (x,y) with (3x,3y), we get
which is equivalent to
Note that comparing the equations 3x-5y=4 and the values of a and b are equal but the value of c is different. This means that they have the same slope but a different y-intercept.