Question

Write the equation in point slope and slope intercept form of a line that passes through the given point and has given slope m.(5,-6);m=-1

Answer 1

Given:

A line passes through the point,

`(x_1,y_1)=(5,-6)`

The slope of the line is m = -1.

The objective is to find the equation of the line in point-slope and slope-intercept form.

Step-by-step explanation:

To find equation in point-slope form:

The general formula of point-slope form is,

`y-y_1=m(x-x_1)\text{ . . . . . . ..(1)}`

On plugging the given values in equation (1),

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

To find the equation in slope-intercept form,

The general formula of slope-intercept form is,

`y=mx+b\text{ . . . . (3)}`

On further solving the equation (2),

`\begin{gathered} y+6=-x+5 \\ y=-x+5-6 \\ y=-x-1 \end{gathered}`

Hence,

The equation of the line in point-slope form is y+6 = -x+5.

The equation of the line in slope-intercept form is y = -x-1.