Question

Find a general form of an equation of the line through the point A that satisfies the given condition.
A(3, −1); parallel to the line 9x − 2y = 4

Answer 1

Hello @kuvyojhmoob ok so your first step is find the slope of the line...

Answer 2

Since it is parallel to the line:
\[ 9x-2y=4 \ \ \ \ \rightarrow \ \ \ \ y=\frac{9}{2}x-2\]
This means their slopes are equivalent. Thus the slope of the desired line is \[ m=\frac{9}{2}\]

Answer 3

Next we know it goes through the point A(3,-1) this means we can calculate the y-intercept as follows. Starting with the slope-intercept form of the equation of a line:
\[y=mx+b\]
and substituting in our know slope m:
\[y=\frac{9}{2}x+b\]
then substitute in our point (3,1) and solve for b:
\[(-1)=\frac{9}{2}(3)+b \ \ \ \ \rightarrow \ \ \ \ b=-1-\frac{9*3}{2}=-(\frac{2+27}{2})=- \frac{29}{2}\]
Putting it all together, the desired eqution of the line:
\[y= \frac{9}{2}x-\frac{29}{2}=\frac{1}{2}(9x-29)\]