Answer:
4) The linear equation which could represent its image is y = [tex]\frac{3}{4}[/tex] x + 8 ⇒ (2)
5) The equation of the image of the line is y = [tex]\frac{3}{2}[/tex] x - 3 ⇒ (4)
Step-by-step explanation:
Dilation does not change the slope of a line but changes the y-intercept
Dilation of a line segment is longer or shorter by ratio that equal to the scale factor of dilation
4)
The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b its y-intercept
Let us put the given equation in the slope-intercept form to find its slope
∵ The line -3x + 4y = 8 is transformed by a dilation centered at
  the origin
- Add 3x to both sides
∴ 4y = 3x + 8
- Divide both sides by 4
∴ y = [tex]\frac{3}{4}[/tex] x + 2 ⇒ the equation of the line before dilation
- By comparing it with the form above, then m = Â [tex]\frac{3}{4}[/tex] , so the
  equation after dilation has the same slope
∵ The slope of the line before dilation is  [tex]\frac{3}{4}[/tex]
∴ The slope of the line after dilation is  [tex]\frac{3}{4}[/tex]
∵ The equation that has the slope  [tex]\frac{3}{4}[/tex]  is y =
∴ The equation of the image of the line is y = [tex]\frac{3}{4}[/tex] x + 8
The linear equation which could represent its image is y = [tex]\frac{3}{4}[/tex] x + 8
5)
∵ The equation of the line is y = [tex]\frac{3}{2}[/tex] x - 4
∵ The scale factor of dilation is [tex]\frac{3}{4}[/tex]
- Dilation dose not change the slope of the line
∴ The slope of the image after dilation is [tex]\frac{3}{2}[/tex]
- Dilation changes the y-intercept, to find it multiply the scale
 factor of dilation by the y-intercept of the line before dilation
∵ The y-intercept of the line is (0 , -4)
- Multiply it by [tex]\frac{3}{4}[/tex]
∵  [tex]\frac{3}{4}[/tex] × -4 = -3
∴ The y-intercept of the image is (0 , -3)
∴ The equation of the image of the line is y = [tex]\frac{3}{2}[/tex] x - 3
