Answer :
Answer:
The equation of dilated line is
y=2x+10
Step-by-step explanation:
Method of dilation:
- When dilating a line a line we need to multiply the y- intercept with the scale factor.The slope of the line remains same.
- putting the new y intercept point in the equation y=mx+b.
- The dilated line is always parallel to the given line.
Given line is
6x-3y=5
[tex]\Rightarrow \frac{6x}{5}-\frac{3y}{5}=1[/tex]
[tex]\Rightarrow 3y=6x-5[/tex]
[tex]\Rightarrow y=2x-\frac53[/tex]
The y-intercept of the line is [tex](0,\frac53)[/tex] and slope of the line is 2
Now multiply the scale factor with the y-intercept.
The point become [tex](0\times 6,\frac53\times 6)=(0,10)[/tex]
Since the slope of the dilated line is 2.
The equation of dilated line is
y=2x+b
The line passes trough the point (0,10). The point will satisfy the equation of line.
∴10=2.0+b
⇒b=10
The equation of dilated line is
y=2x+10
The equation after dilating the function is: [tex]y = 2x - 10[/tex]
The equation is given as:
[tex]6x - 3y = 5[/tex]
Subtract 6x from both sides
[tex]- 3y = -6x + 5[/tex]
Divide through by -3
[tex]y = 2x - \frac{5}{3}[/tex]
To dilate by a scale factor of 6, we simply multiply the y-intercept by the scale factor.
So, we have:
[tex]y = 2x - \frac{5}{3} \times 6[/tex]
Evaluate the product
[tex]y = 2x - 5\times 2[/tex]
[tex]y = 2x - 10[/tex]
Hence, the equation after dilating the function is: [tex]y = 2x - 10[/tex]
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