How do you write an equation for a line that is parallel to #y=3x+7# and passes through (2,10)?

Question

Kennedy Adams · Accepted Answer

#y=3x+4# #y=mx+b# Where #m# is the slope and #b# is the y intercept The slope of the given equation, #y=3x+7# is #3# So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of #3#: #y-y_1=m(x-x_1)# Where #(2,10)=>(x_1,y_1)# and #m=3# #y-10=3(x-2)# Distribute the #3# throughout the set of parenthesis #y-10=3x-6# Perform the opposite operation to isolate #y# by adding #10# on both sides of the equation #y=3x+4# As you can see, the slope of this line is #3#, which means that the two equations are parallel to each other

Jace Anderson · Answer

undefined To write an equation for a line that is parallel to $y = 3x + 7$ and passes through the point $(2, 10)$, we first need to determine the slope of the given line, which is $3$. Since parallel lines have the same slope, the slope of the parallel line will also be $3$.

Now that we have the slope, we can use the point-slope form of a linear equation:

$y - y_1 = m(x - x_1)$

Substitute the values of $m$ (slope) and $(x_1, y_1)$ (the given point):

$y - 10 = 3(x - 2)$

Simplify:

$y - 10 = 3x - 6$

Add $10$ to both sides:

$y = 3x + 4$

This is the equation for the line parallel to $y = 3x + 7$ that passes through the point $(2, 10)$.