Given :-
To Find :-
Solution :-
Here it's given that ,
[tex]\longrightarrow m =\dfrac{-3}{2}[/tex]
And a point that is (-3,3) . We can use the point slope form of the line which is ,
[tex]\longrightarrow y - y_1 = m(x - x_1) [/tex]
Substituting the respective values,
[tex]\longrightarrow y - 3 = \dfrac{-3}{2}\{ x -(-3)\}[/tex]
Simplify,
[tex]\longrightarrow y -3 = \dfrac{-3}{2}( x +3)[/tex]
Simplify by opening the brackets ,
[tex]\longrightarrow y - 3 =\dfrac{-3}{2}x -\dfrac{9}{2} [/tex]
Add 3 on both sides ,
[tex]\longrightarrow y = \dfrac{-3}{2}x -\dfrac{9}{2}+3[/tex]
Add ,
[tex]\longrightarrow \underline{\underline{ y =\dfrac{-3}{2}x -\dfrac{3}{2}}} [/tex]
This is the required answer in slope intercept form .
Based on given conditions,
[tex]m = - \frac{3}{2} [/tex]
Substitute,
[tex]m = - \frac{3}{2} \\ x = - 3 \: \: \: into \\ y = 3[/tex]
So,
[tex]y = mx + b[/tex]
[tex] = > 3 = - \frac{3}{2} \times ( - 3) + b[/tex]
As signs are both minus, write,
[tex] 3 = \frac{3 \times 3}{2} + b[/tex]
[tex] = > 3 = \frac{9}{2} + b[/tex]
Rearranging equations,
[tex] = > - b = \frac{9}{2} - 3[/tex]
Findind LCM as 2,
[tex] = > - b = \frac{9}{2} \times \frac{3 \times 2}{1 \times 2} [/tex]
[tex] = > - b = \frac{9 - 6}{2}[/tex]
[tex] = > - b = \frac{3}{2} [/tex]
[tex] = > b = - \frac{3}{2} [/tex]
Now substitute,
[tex]m = - \frac{ 3}{2} \: \: \: into \\ b = - \frac{3}{2} [/tex]
So,
[tex]y = mx + b[/tex]
[tex] = > y = - \frac{3}{2} \times x + \frac{ - 3}{2} [/tex]
Rewriting in slope intercept form:
(Please check attached image)
