Question

Write an equation in slope-intercept form of a line passingthrough the given point and perpendicular to the given line.(3, 4); 2x+y=1

Answer 1

The point is given (3, 4) and the given line is 2x+y=1.

The line to be determined is passes through the point and the perpendicular to the given line 2x+y=1.

So the slope of the line will be

`m_1* m_2=-1`
`m_1*-2=-1`
`m_1=(1)/(2)`

The slope-intercept form of a line is

`y-y_1=m(x-x_1)`
`y-4=(1)/(2)(x-3)`
`y=(1)/(2)x-(3)/(2)+4`
`y=(1)/(2)x+4-(3)/(2)`
`y=(1)/(2)x+(8-3)/(2)`
`y=(1)/(2)x+(5)/(2)`

Hence the equation in slope -intercept form of a line is

`y=(1)/(2)x+(5)/(2)`