How do you write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1?
1 Answer
May 29, 2016
Explanation:
The equation of a line in
#color(blue)"slope-intercept form"# is
#color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))#
where m represents the gradient and b, the y-intercept.The advantage of having the line in this form is that m and b can be extracted 'easily'
The equation : y = - 3x + 1 is in this form
hence m = - 3
If 2 lines are perpendicular then the product of their gradients .
#m_1" and " m_2", say," # is -1
#color(red)(|bar(ul(color(white)(a/a)color(black)(m_1.m_2=-1)color(white)(a/a)|)))# hence gradient of perpendicular line is
#1/3" since "(3xx-1/3=-1)# We have y-intercept = b = 5 and m
#=1/3#
#rArry=1/3x+5" is the equation"#
graph{(y+3x-1)(y-1/3x-5)=0 [-20, 20, -10, 10]}
