Respuesta :
Answer:
The equation of the straight line in point-slope form
[tex]y - 4 = \frac{7}{9} (x-0)[/tex]
The equation of the straight line
7x -9y +36 =0
Step-by-step explanation:
Step(i):-
Given that the points (0,4) and (-9,-3)
The slope of the line
[tex]m = \frac{y_{2} - y_{1} }{x_{2}- x_{1} } = \frac{-3-4}{-9-0} = \frac{7}{9}[/tex]
Step(ii):-
Equation of the straight line passing through the point (0,4) and having slope m = 7/9
[tex]y - y_{1} = m (x-x_{1} )[/tex]
[tex]y - 4 = \frac{7}{9} (x-0)[/tex]
9 y - 36 = 7x
9y = 7x + 36
[tex]y = \frac{7x}{9} +\frac{36}{9}[/tex]
Slope - intercept form
[tex]y = \frac{7x}{9} +4[/tex]
Final answer:-
The equation of the straight line in point-slope form
[tex]y - 4 = \frac{7}{9} (x-0)[/tex]
The equation of the straight line
7x -9y +36 =0
