Question

Sketch the lines through the point with the indicated slopes on the same set of coordinate axes.

Point (-3 -2) (a) 3 (b) -5 (c) 2/3 (d) undefined

Answer 1

negative = down or left positive = up or right

Answer 2

Answer with explanation:

Equation of a line passing through point (a,b) and has a slope m is given by :-

`(y-b)=m(x-a)`

From the given picture , given point = (-3,2)

a) Equation of a line passing through point (-3 ,2) and has a slope 3 is given by :-

`(y-(2))=3(x-(-3))\\\\\Rightarrow\ y-2=3(x+3)\\\\\Rightarrow\ y=3x+9+2\\\\\Rightarrow\ y=3x+11`

b) Equation of a line passing through point (-3 ,2) and has a slope -5 is given by :-

`(y-(2))=-5(x-(-3))\\\\\Rightarrow\ y-2=-5(x+3)\\\\\Rightarrow\ y=-5x-15+2\\\\\Rightarrow\ y=-5x-13`

c) Equation of a line passing through point (-3 ,2) and has a slope
`(2)/(3)`is given by :-

`(y-(2))=(2)/(3)(x-(-3))\\\\\Rightarrow\ y-2=(2)/(3)(x+3)\\\\\Rightarrow\ y=(2)/(3)x+2+2\\\\\Rightarrow\ y=(2)/(3)x+4`

We know that when slope is undefined , then the line is parallel to y axis.

d) The line parallel to y axis and passes through given point : x=-3

[Note , when slope is undefined , it means x-values does not change through out the line ∵ slope =
`\frac{\text{Change in y values}}{\text{Change in x-values}}`]