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.