# lines an equations

• Jan 14th 2006, 09:08 AM
pianogurl1250
lines an equations
ok another question...

i need to find out an equation of a line that contains the point (-2,5) and is parallel to the line y=4x-3

• Jan 14th 2006, 09:18 AM
TD!
If the equation of a line is of the form y = ax + b, then a is the slope.
Find the slope of the given line, since parallel lines have the same slope, you have then found a.
To determine b, fill in the given point for x and y, this will give a lineair equation in b which you can solve.

Also possible: the line with slope a through the point (p,q) is given by: y-q = a(x-p).
• Jan 14th 2006, 09:21 AM
CaptainBlack
Quote:

Originally Posted by pianogurl1250
ok another question...

i need to find out an equation of a line that contains the point (-2,5) and is parallel to the line y=4x-3

A line parallel to $\displaystyle y=4x-3$ has slope or gradient equal to the
gradient of this line, so the required gradient is $\displaystyle 4$.

Therefore the equation of the line is something like:

$\displaystyle y=4x+c$,

for some $\displaystyle c$. The value of $\displaystyle c$ can be determined as
it passes through $\displaystyle (-2,5)$. To do this we put $\displaystyle y=5$ and
$\displaystyle x=-2$ into the above equation and then solve for $\displaystyle c$, ie solve:

$\displaystyle 5=4 \times (-2) +c$

for $\displaystyle c$.

RonL