Write the equation of a line in slope-intercept form that is parallel to the line y = 3x +2 and passes through the point (5, 2).

To find the equation of a line that is parallel to y = 3x + 2, we know that the slope of the new line will also be 3.

Using the point-slope form of a linear equation, we can write the equation as:

y - y1 = m(x - x1)

where (x1, y1) represents the given point (5, 2) and m is the slope.

Plugging in the values we have, the equation becomes:

y - 2 = 3(x - 5)

Expanding the equation, we get:

y - 2 = 3x - 15

or

y = 3x - 13

So, the equation of the line parallel to y = 3x + 2 and passing through the point (5, 2) is y = 3x - 13.

To find the equation of a line that is parallel to y = 3x + 2 and passes through the point (5, 2), we can use the fact that parallel lines have the same slope.

The given line y = 3x + 2 is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

In this case, the given line has a slope of 3. Therefore, the parallel line we are looking for will also have a slope of 3.

Now that we know the slope for the parallel line, we can use the point-slope form of a linear equation to find the equation of this line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Using the point (5, 2), we can substitute the values into the equation:

y - 2 = 3(x - 5)

Now, we can simplify and rearrange the equation to find it in slope-intercept form:

y - 2 = 3x - 15

Adding 2 to both sides:

y = 3x - 13

Therefore, the equation of the line that is parallel to y = 3x + 2 and passes through the point (5, 2) is y = 3x - 13.

y = mx + b

2 = 3*5 + b
b = -13

y = 3x - 13

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