Respuesta :
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 [tex]ax+by=c[/tex]. From this equation, the slope of the line is given by the number [tex]\frac{-a}{b}[/tex] and the y-intercept is given by [tex]\frac{c}{b}[/tex].
Consider the given equation 3x-5y =4. If we replace (x,y) with (3x,3y), we get
[tex]3(3x)-5(3y) = 4 = 3 (3x-5y) = 4 [/tex]
which is equivalent to
[tex] 3x-5y = \frac{4}{3}[/tex]
Note that comparing the equations 3x-5y=4 and [tex]3x-5y=\frac{4}{3}[/tex] 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.
