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Determine the equation of the line that passes through the points (0, 0) and (3,
Determine the equation of the line that passes through the points (0, 0) and (3, 9).
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Practice Questions
1 question
Q1
Determine the equation of the line that passes through the points (0, 0) and (3, 9).
y = 3x
y = 2x
y = 3x + 1
y = x + 1
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The slope m = (9 - 0) / (3 - 0) = 3. The equation is y = 3x.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the equation of the line that passes through the points (0, 0) and (3, 9).
Solution:
The slope m = (9 - 0) / (3 - 0) = 3. The equation is y = 3x.
Steps: 8
Show Steps
Step 1: Identify the two points given. The points are (0, 0) and (3, 9).
Step 2: Use the formula for slope (m) which is (y2 - y1) / (x2 - x1). Here, (x1, y1) = (0, 0) and (x2, y2) = (3, 9).
Step 3: Substitute the values into the slope formula: m = (9 - 0) / (3 - 0).
Step 4: Calculate the slope: m = 9 / 3 = 3.
Step 5: Use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Step 6: Since the line passes through the origin (0, 0), the y-intercept (b) is 0.
Step 7: Substitute the slope and y-intercept into the equation: y = 3x + 0.
Step 8: Simplify the equation to get the final equation of the line: y = 3x.
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