On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she ha
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4) The linear equation which could represent its image is y = x + 8 ⇒ (2)
5) The equation of the image of the line is y = 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 = x + 2 ⇒ the equation of the line before dilation
- By comparing it with the form above, then m = , so the
equation after dilation has the same slope
∵ The slope of the line before dilation is
∴ The slope of the line after dilation is
∵ The equation that has the slope is y =
∴ The equation of the image of the line is y = x + 8
The linear equation which could represent its image is y = x + 8
5)
∵ The equation of the line is y = x - 4
∵ The scale factor of dilation is
- Dilation dose not change the slope of the line
∴ The slope of the image after dilation is
- 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
∵ × -4 = -3
∴ The y-intercept of the image is (0 , -3)
∴ The equation of the image of the line is y = x - 3