How to determine the equation of the line parallel to 3x - 2y + 4 = 0 and passing through (1,6)?
2 Answers
Explanation:
color(orange)"Reminder "color(red)(bar(ul(|color(white)(2/2)color(black)("parallel lines have equal slope")color(white)(2/2)|))) The equation of a line in
color(blue)"slope-intercept form" is.
color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))
where m represents the slope and b, the y-intercept.
"Rearrange "3x-2y+4=0" into this form" add 2y to both sides.
3xcancel(-2y)cancel(+2y)+4=0+2y
rArr2y=3x+4 divide ALL terms on both sides by 2
(cancel(2) y)/cancel(2)=3/2x+4/2
rArry=3/2x+2larr" in form "y=mx+b
rArr"slope "=m=3/2 The equation of a line in
color(blue)"point-slope form" is.
color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))
m is slope and(x_1,y_1)" a point on the line"
"For parallel line " m=3/2" and " (x_1,y_1)=(1,6)
rArry-6=3/2(x-1)larrcolor(red)" in point-slope form" Distributing the bracket and simplifying gives the equation in an alternative form.
y-6=3/2x-3/2
rArry=3/2x-3/2+6
rArry=3/2x+9/2larrcolor(red)" in slope-intercept form"
graph{(y-3/2x-2)(y-3/2x-9/2)=0 [-10, 10, -5, 5]}
Explanation:
Recall that the eqn. of a line parallel to the given line
If we compare the slopes of the lines
the result is quite obvious. If, in addition, #(x_0,y_0) in l_2, then,
Accordingly, the eqn. of the reqd. line is given by,