Question 221025


We can see that the equation {{{y=(3/7)x-2}}} has a slope {{{m=3/7}}} and a y-intercept {{{b=-2}}}.



Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is {{{m=3/7}}}.

Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope {{{m=3/7}}}  and the coordinates of the given point *[Tex \LARGE \left\(4,0\right\)].



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y-0=(3/7)(x-4)}}} Plug in {{{m=3/7}}}, {{{x[1]=4}}}, and {{{y[1]=0}}}



{{{y=(3/7)(x-4)}}} Simplify



{{{y=(3/7)x+(3/7)(-4)}}} Distribute



{{{y=(3/7)x-12/7}}} Multiply



So the equation of the line parallel to {{{y=3/7x-2}}} that goes through the point *[Tex \LARGE \left\(4,0\right\)] is {{{y=(3/7)x-12/7}}}.



Here's a graph to visually verify our answer:

{{{drawing(500, 500, -10, 10, -10, 10,
graph(500, 500, -10, 10, -10, 10,(3/7)x-2,(3/7)x-12/7),
circle(4,0,0.08),
circle(4,0,0.10),
circle(4,0,0.12))}}}Graph of the original equation {{{y=(3/7)x-2}}} (red) and the parallel line {{{y=(3/7)x-12/7}}} (green) through the point *[Tex \LARGE \left\(4,0\right\)].