Question

Graph the line with slope2/3 passing through the point(-2, 1)

Answer 1

The graph in the attached figure

Explanation:

step 1

Find the equation of the line into point slope form

The equation of the line is equal to

`y-y1=m(x-x1)`

substitute the given values

`y-1=(2/3)(x+2)`

step 2

To graph the line find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

`y-1=(2/3)(0+2)`

`y=(4/3)+1`

`y=(7/3)`

The y-intercept is the point (0,7/3)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

`0-1=(2/3)(x+2)`

`-1=(2/3)x+(4/3)`

`(2/3)x=-(4/3)-1`

`(2/3)x=-(7/3)`

`2x=-7`

`x=-7/2`

The x-intercept is the point (-7/2,0)

step 3

Plot the intercepts to graph the line

see the attached figure