What is an equation of the line that passes through the point (-1,-3)(−1,−3) and is parallel to the line 6x-y=16x−y=1?
\text{Solve for y:}
Solve for y:
Put into slope-intercept form
6x-y=
6x−y=
\,\,1
1
-6x\color{transparent}{-y}\phantom{=}
−6x−y=
\,\,-6x
−6x
Bring x's to the right
-y=
−y=
\,\,-6x+1
−6x+1
\frac{-y}{-1}=
−1
−y
​
=
\,\,\frac{-6x+1}{-1}
−1
−6x+1
​

Divide by -1
y=
y=
\,\,6x-1
6x−1
Distribute division
\text{Slope of given line: }6
Slope of given line: 6
The coefficient of x is the slope
\text{Slope of a parallel line: }6
Slope of a parallel line: 6
Parallel slopes are equal
\text{Slope Intercept Form: }
Slope Intercept Form:
y=mx+b
y=mx+b
\text{(m: slope, b: y-intercept)}
(m: slope, b: y-intercept)
y=6x+b
y=6x+b
Plug in slope.
\text{Find b: plug in point }(-1, -3)
Find b: plug in point (−1,−3)
Given
\hspace{50px}-3=
−3=
\,\,6(-1)+b
6(−1)+b
\hspace{50px}-3=
−3=
\,\,-6+b
−6+b
Multiply.
\hspace{50px}+6\phantom{=}
+6=
\,\,+6
+6
\hspace{50px}3=
3=
\,\,b
b
We found b!
\text{Plug b in to original formula:}
Plug b in to original formula:
y=6x+3
y=6x+3
Final equation.
\text{The line goes through }(-1,-3) \text{ and is}
The line goes through (−1,−3) and is
\text{parallel to the line }6x-y=1
parallel to the line 6x−y=1
Final answer:
y=6x+3