Answer:
[tex]y= \frac{5}{9}x - 2[/tex]
Step-by-step explanation:
Let's write the equation in the slope-intercept form! In the slope-intercept form, y= mx +c, m is the slope and c is the y-intercept.
[tex]\textcolor{blueviolet}{\text{\textcircled{1} Find \: the \: slope}}[/tex]
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
Slope
[tex] = \frac{ - 2 - ( - 7)}{0 - ( - 9)} [/tex]
[tex] = \frac{ - 2 + 7}{0 + 9} [/tex]
[tex] = \frac{5}{9} [/tex]
[tex]\textcolor{blueviolet}{\text{\textcircled{2} Substitute \: value \: of \: slope}}[/tex]
[tex]y = \frac{5}{9} x + c[/tex]
[tex]\textcolor{blueviolet}{\text{\textcircled{3} Substitute \: a \: pair \: of \: coordinates}}[/tex]
When x= 0, y= -2,
[tex] - 2 = \frac{5}{9} (0) + c[/tex]
c= -2
[tex]\textcolor{blueviolet}{\text{\textcircled{4} Substitute \: value \: of \: c}}[/tex]
[tex]\bf y= \frac{5}{9}x - 2[/tex]
