## kuvyojhmoob one year ago 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

1. anonymous

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

2. anonymous

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 $m=\frac{9}{2}$

3. anonymous

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: $y= \frac{9}{2}x-\frac{29}{2}=\frac{1}{2}(9x-29)$