Answer:
[tex]y = \frac{11}{13} x + 2 \frac{10}{13} [/tex]
Step-by-step explanation:
y= mx +c, where m is the slope and c is the y-intercept.
We need to find the value of m and c, which can be done by using the slope formula and by substituting a pair of coordinates respectively. Find m first before finding the value of c.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
[tex]slope = \frac{7 - ( - 4)}{5 - ( - 8)} [/tex]
[tex]slope = \frac{7 + 4}{5 + 8} [/tex]
[tex]slope = \frac{11}{13} [/tex]
Substitute the value of m into the equation:
[tex]y = \frac{11}{13} x + c[/tex]
Substitute a pair of coordinates:
When x= 5, y= 7,
[tex]7 = \frac{11}{13} (5) + c[/tex]
[tex]c = 7 - \frac{55}{13} [/tex]
[tex]c = \frac{91}{13} - \frac{55}{13} [/tex]
[tex]c = \frac{36}{13} [/tex]
[tex]c = 2 \frac{10}{13} [/tex]
Thus, the equation of the line is [tex]y = \frac{11}{13} x + 2 \frac{10}{13} [/tex].
