You should remember the relation between the slopes of two orthogonal lines such that: `m_1*m_2=-1` .
Notice that the slope intercept form of the line `y=(-1/3)x - ` 4 gives the slope `m_1 = -1/3` , hence `m_2 = -1/(-1/3) =gt m_2 = 3` .
You need to write the slope intercept form of the line that passes through (6,1), with `m_2=3` such that:
`y - 1 = 3(x - 6)`
Opening the brackets yields:
`y - 1 = 3x - 18 =gt y = 3x - 18 + 1`
`y = 3x - 17`
Hence, the slope intercept form of equation of the line, orthogonal to `y=(-1/3)x - 4` is `y = 3x - 17` .
a line through (6,1) and perpendicular to the line y=-1/3x-4
The slope of the original line is -1/3. The slope of a line perpendicular to this is the negative reciprocal: 3
We want a line that goes through the points (6,1) with slope of 3. Writing this in point-slope form is easiest.
y - y1 = m(x - x1)
y - 1 = 3(x - 6)
To get this into slope-intercept form, just solve for y and make sure to distribute the slope.
y = 3x - 18 + 1
y = 3x - 17