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Y=2/3x+5 dialated by a scale factor of 10

A:y=20/30x+5
B:y=2/3x+50
C:y=2/3x+5
D:y=2/3x+1

User Nerdherd
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1 Answer

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The original line y = 2/3x + 5 was dilated by a scale factor of 10. The slope remained the same, but the y-intercept was multiplied by 10, resulting in the equation y = 2/3x + 50.

The correct answer is option B. "y = 2/3x + 50."

Determining the equation of the dilated line:

We are given the equation of the original line: y = 2/3x + 5. We need to find the equation of the line after it is dilated by a scale factor of 10.

Dilation rules:

Dilation preserves the slope of the line.

Dilation multiplies the y-intercept by the scale factor.

Step 1: Identify the slope and y-intercept of the original line.

Comparing the given equation with the slope-intercept form (y = mx + b), we can identify:

Slope (m) = 2/3

Y-intercept (b) = 5

Step 2: Apply dilation rules.

Slope (m) remains unchanged: m' = 2/3

Y-intercept (b') is multiplied by the scale factor (10): b' = 5 * 10 = 50

Step 3: Write the equation of the dilated line.

Using the slope (m') and y-intercept (b'), we can write the equation of the dilated line:

y = 2/3x + 50

Checking the answer choices:

Option A: y = 20/30x + 5 is incorrect. The slope is correct, but the y-intercept is not (50 instead of 5).

Option B: y = 2/3x + 50 is correct. This matches the equation we derived.

Option C: y = 2/3x + 5 is the original equation and not the dilated one.

Option D: y = 2/3x + 1 is incorrect. Both the slope and y-intercept are different from the dilated line.

User Robert Swisher
by
8.1k points
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