Final answer:
To find the equation of a line when dilated by a scale factor of 5 centered at the origin, we need to apply the dilation transformation to the given line equation.
Step-by-step explanation:
To find the equation of a line when dilated by a scale factor of 5 centered at the origin, we need to apply the dilation transformation to the given line equation. The scale factor of 5 means that all the coordinates of the line will be multiplied by 5. Let's start by rewriting the given equation in slope-intercept form.
4y - 2x = 8
First, we isolate y by moving -2x to the other side of the equation:
4y = 2x + 8
Next, we divide both sides by 4 to solve for y:
y = (2/4)x + 8/4
Simplifying further:
y = (1/2)x + 2
Now, we can apply the dilation transformation by multiplying the x and y coefficients by the scale factor of 5:
y = (5/2)x + 10