Find the equation of the line that passes through the point (1, 2) and has a slo

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Question: Find the equation of the line that passes through the point (1, 2) and has a slope of 3.

Options:

Correct Answer: y = 3x + 2

Solution:

Using point-slope form: y - 2 = 3(x - 1) => y = 3x - 1.

Find the equation of the line that passes through the point (1, 2) and has a slope of 3.

Find the equation of the line that passes through the point (1, 2) and has a slope of 3.

Step 1: Identify the point the line passes through, which is (1, 2). This means x = 1 and y = 2.
Step 2: Identify the slope of the line, which is given as 3.
Step 3: Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.
Step 4: Substitute the values into the point-slope form: y - 2 = 3(x - 1).
Step 5: Simplify the equation. Start by distributing the 3: y - 2 = 3x - 3.
Step 6: Add 2 to both sides to solve for y: y = 3x - 3 + 2.
Step 7: Combine like terms: y = 3x - 1.
Step 8: The final equation of the line is y = 3x - 1.

Point-Slope Form – The equation of a line can be expressed using the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Slope-Intercept Form – The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.