Question

Write the equation of a line that is parallel to Y =3x-2 that passes through (4,1)

Answer 1

The equation of the line is y = 3x - 11.

Explanation:

We are given the equation of a line:

`\bullet \ \ \ y = 3x -2`

We are also given a point at which the line passes through.

`\bullet \ \ \ (4, 1)`

With parallel lines, it is important to note:

• Parallel lines have the same slope.
• Parallel lines must have a different y-intercept.

We can use the point-slope equation to find the equation of the line:

`\displaystyle y-y_1 =m(x-x_1)\\\\y - 1 = 3(x - 4)\\\\y - 1 = 3x - 12\\\\y - 1 + 1 = 3x - 12 + 1\\\\y = 3x - 11`

Therefore, the line that is parallel to y = 3x - 2 and passes through the point (4, 1) is y = 3x - 11.