orWatch a videoLine 𝓁 has the equation y=–5x–1. Write the equation of the image of 𝓁 after a dilation with a scale factor of 3, centered at the origin.Write your answer in slope-intercept form.
Question
orWatch a videoLine 𝓁 has the equation y=–5x–1. Write the equation of the image of 𝓁 after a dilation with a scale factor of 3, centered at the origin.Write your answer in slope-intercept form.
Solution
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
The given line has the equation y = -5x - 1, so its slope is -5 and its y-intercept is -1.
A dilation with a scale factor of 3, centered at the origin, multiplies all y-coordinates by 3. This means that the slope and the y-intercept of the line will also be multiplied by 3.
So, the slope of the dilated line is -5 * 3 = -15, and the y-intercept of the dilated line is -1 * 3 = -3.
Therefore, the equation of the image of the line after the dilation is y = -15x - 3.
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