Question

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

Answer 1

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 $\dfrac{2}{3}$is given by :-

$(y-(2))=\dfrac{2}{3}(x-(-3))\\\\\Rightarrow\ y-2=\dfrac{2}{3}(x+3)\\\\\Rightarrow\ y=\dfrac{2}{3}x+2+2\\\\\Rightarrow\ y=\dfrac{2}{3}x+4$

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 = $\dfrac{\text{Change in y values}}{\text{Change in x-values}}$]

Answer 2

negative = down or left             positive = up or right