The equation of a line with slope 2 passing through the point (1, 3) is?

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Question: The equation of a line with slope 2 passing through the point (1, 3) is?

Options:

Correct Answer: y = 2x + 3

Solution:

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

The equation of a line with slope 2 passing through the point (1, 3) is?

The equation of a line with slope 2 passing through the point (1, 3) is?

Step 1: Identify the slope of the line, which is given as 2.
Step 2: Identify the point through which the line passes, which is (1, 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 - 3 = 2(x - 1).
Step 5: Simplify the equation. Start by distributing the 2: y - 3 = 2x - 2.
Step 6: Add 3 to both sides to isolate y: y = 2x - 2 + 3.
Step 7: Combine like terms: y = 2x + 1.
Step 8: The final equation of the line is y = 2x + 1.

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