Line l has the equation y=1/2x-4. Write the equation of the image of l after a dilation with a scale factor of 1/4 centered at the origin.
Write your answer in slope-intercept form?
To write the equation of the image of line l after a dilation with a scale factor of 1/4 centered at the origin, we need to multiply the original equation's slope by the scale factor.
Given the original equation of line l: y = (1/2)x - 4
Step 1: Find the new slope
The scale factor is 1/4, so the new slope will be (1/2) * (1/4) = 1/8.
Step 2: Find the new y-intercept
Since the dilation is centered at the origin (0,0), the image will also intersect the y-axis at (0,0). Therefore, the y-intercept remains the same.
Step 3: Write the equation in slope-intercept form
The new equation of the image of line l after dilation is y = (1/8)x - 4.
Thus, the equation of the image of line l after a dilation with a scale factor of 1/4 centered at the origin is y = (1/8)x - 4.
To find the equation of the image of line l after dilation with a scale factor of 1/4 centered at the origin, we need to apply the following transformation to line l: multiply the slope by the scale factor, and multiply the y-intercept by the scale factor as well.
The given equation of line l is y = (1/2)x - 4.
Step 1: Scale the slope.
The scale factor is 1/4. Multiply the slope of line l by the scale factor:
(1/2) * (1/4) = 1/8.
Step 2: Scale the y-intercept.
The y-intercept of line l is -4. Multiply the y-intercept by the scale factor:
-4 * (1/4) = -1.
Therefore, the equation of the image of line l after dilation with a scale factor of 1/4 centered at the origin is:
y = (1/8)x - 1.
Written in slope-intercept form, the equation is y = (1/8)x - 1.