Question

line p contains point (6 ,- 5 and is perpendicular to line q the equation for line q is y=3x+5 the slope of line q is 3. the slope of line p is -1/3. Equation for line p in point slope form is y = -1/3x - 3) Use your equation to write an equation for line p in slope-intercept form

Answer 1

Given:

Line p contains the point (6,- 5 and is perpendicular to line q the equation for line q is y=3x+5 the slope of line q is 3. and the slope of line p is -1/3. Equation for line p in point-slope form is y = -1/3x - 3.

Required:

Write an equation for line p in slope-intercept form.

Step-by-step explanation:

The equation of line q is:

`y=3x+5`

The line p is perpendicular to line q.

The slope of line q = 3

We know that the perpendicular line has negative reciprocal slopes.

So the slope of line p

`=(-1)/(3)`

The equation of line has slope m and passes through from one point is given as:

`y-y_1=m(x-x_1)`
`(x_1,y_1)=(6,-5)`

Thus the equation of line p is:

`\begin{gathered} y-(-5)=-(1)/(3)(x-6) \\ y+5=-(1)/(3)x+2 \\ y=-(1)/(3)x-3 \end{gathered}`

Final Answer:

The equation of line p is:

`y=-(1)/(3)x-3`