Question

The equation of the line passing through (1, 2) and parallel to the line y = 3x + 5 is:

• A. y = 3x − 1
• B. y = 3x + 2
• C. y = 3x + 1
• D. y = −3x + 2

Answer 1

Answer: (A)

y = 3x − 1

Answer 2

To find the equation of a line parallel to a given line and passing through a specific point, we follow these steps:

1. Identify the slope of the given line: The given line is in the form $y = mx + c$, where $m$ is the slope. In the equation $y = 3x + 5$, the slope is $m = 3$.

2. Parallel lines have the same slope: Therefore, the line we are looking for also has a slope of $3$.

3. Use the point-slope form or slope-intercept form: We know the slope ($m = 3$) and a point the line passes through ($(x_1, y_1) = (1, 2)$).

   Method 1: Using slope-intercept form ($y = mx + c$) Substitute the slope $m = 3$ into the equation: $y = 3x + c$ Now, substitute the coordinates of the point $(1, 2)$ into this equation to find $c$: $2 = 3(1) + c$ $2 = 3 + c$ $c = 2 - 3$ $c = -1$ So, the equation of the line is $y = 3x - 1$.

   Method 2: Using point-slope form ($y - y_1 = m(x - x_1)$) Substitute $m = 3$, $x_1 = 1$, and $y_1 = 2$ into the point-slope form: $y - 2 = 3(x - 1)$ $y - 2 = 3x - 3$ $y = 3x - 3 + 2$ $y = 3x - 1$

Therefore, the equation of the line is $y = 3x - 1$.