How do you the equation of the line that is parallel to the line y = 3x +2 and passes through the point (5, 2)?

Question

Abigail Allen · Accepted Answer

#y=3x-13# The slope(#S#) of the two parallel line will be the same #S=3# So the other line would be #y=3x+k#, bring in (5, 2) to solve #k# #2=3*5+k->k=-13->y=3x-13#

Abigail Allen · Answer

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

Since the given line $y = 3x + 2$ has a slope of $3$, the parallel line will also have a slope of $3$.

Now, using the point-slope form of a linear equation $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point and $m$ is the slope:

$$y - 2 = 3(x - 5)$$

$$y - 2 = 3x - 15$$

$$y = 3x - 13$$

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

Jace Anderson · Answer

undefined To find the equation of a line parallel to $y = 3x + 2$ and passing through the point $(5, 2)$, we know that parallel lines have the same slope. Therefore, the slope of the parallel line will be $3$.

Using the point-slope form of the equation of a line $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line, we can substitute the given values into the equation:

$y - 2 = 3(x - 5)$

Now, simplify and solve for $y$:

$y - 2 = 3x - 15$

$y = 3x - 15 + 2$

$y = 3x - 13$

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