Determine the equation of the line that passes through the points (0, 0) and (3,

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Question: Determine the equation of the line that passes through the points (0, 0) and (3, 9).

Options:

Correct Answer: y = 3x

Solution:

The slope m = (9 - 0) / (3 - 0) = 3. The equation is y = 3x.

Determine the equation of the line that passes through the points (0, 0) and (3, 9).

Determine the equation of the line that passes through the points (0, 0) and (3, 9).

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.

Slope Calculation – Understanding how to calculate the slope of a line using two points.
Point-Slope Form – Using the slope and a point to derive the equation of a line.
Linear Equation – Formulating the equation of a line in the slope-intercept form (y = mx + b).