Answer :
Answer:
[tex]y = \frac{5}{2} + \frac{19}{2}[/tex]
Step-by-step explanation:
From the question;
- We are given, two points; (-7,-8) and (-5,-3)
We are required to determine the equation of a line that passes through points (-7,-8) and (-5,-3).
Note that we can get the equation of a line when;
- We are given two points where the line is passing through
- We are given the slope of the line and one point where the line is passing through
Therefore, since we are given two points where the line is passing through we can get the equation;
First, we determine the slope of the line;
slope = change in y ÷ change in x
That is;
[tex]slope=\frac{(-3--8)}{(-5--7)}[/tex]
[tex]=\frac{5}{2}[/tex]
Second, we take another point (x,y) and one of the points, in this case, we take (-5,-3).
Therefore;
[tex]\frac{y+3}{x+5}=\frac{5}{2}[/tex]
[tex]2(y+3)=5(x+5)\\2y + 6 = 5x +25\\2y= 5x + 19\\y = \frac{5}{2} + \frac{19}{2}[/tex]
Therefore, the equation of the line is [tex]y = \frac{5}{2} + \frac{19}{2}[/tex]