Answer:
[tex]y=-\frac{3}{2}x+12[/tex]
Step-by-step explanation:
Hi there!
We want to write the equation of a line parallel to y=[tex]-\frac{3}{2}x-1[/tex] and that passes through the point (4,6)
Parallel lines have the same slopes, but different y intercepts.
The slope of the equation [tex]y=-\frac{3}{2}x-1[/tex] is [tex]-\frac{3}{2}[/tex], since the equation is written in y=mx+b format (m is slope and b is y intercept), and [tex]-\frac{3}{2}[/tex] is in the place where m is.
It's also the slope of the line parallel to it.
So we know the slope of the new line, let's write it down:
y=[tex]-\frac{3}{2}x[/tex]+b
Let's find b, in order to complete the equation
Since the equation passes through the point (4, 6), we can use it to solve for b.
Substitute 4 as x and 6 as y into the equation:
6=[tex]-\frac{3}{2}[/tex](4)+b
Multiply
6=-6+b
Add 6 to both sides
12=b
Substitute 12 as b in the equation.
y=[tex]-\frac{3}{2}x+12[/tex]
Hope this helps!
