For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
We have the following equation:
[tex]5x-4y = -7[/tex]
We manipulate algebraically to write the equation of the slope-intersection form:
[tex]-4y = -7-5x\\4y = 5x + 7\\y = \frac {5} {4} x + \frac {7} {4}[/tex]
We check if the given point belongs to the equation:
[tex]y = \frac {5} {4} (- 20) + \frac {7} {4}\\y = -25 + \frac {7} {4}\\y = \frac {-100 + 7} {4}\\y = - \frac {93} {4}[/tex]
The point does not belong to the equation.
ANswer:
[tex]y = \frac {5} {4} x + \frac {7} {4}[/tex]
