Answer:
[tex]y = \frac{3}{2} x + 4 \frac{1}{2} [/tex]
Step-by-step explanation:
y=mx+c
where m is the gradient and c is the y-intercept of the line
Let's find the gradient of the line first.
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Using the above formula,
[tex]gradient \: of \: line \\ = \frac{3 - ( - 3)}{ - 1 - ( - 5)} \\ = \frac{3 + 3}{5 - 1} \\ = \frac{6}{4} \\ = \frac{3}{2} [/tex]
Subst. the gradient into m:
[tex]y = \frac{3}{2} x + c[/tex]
Now, find the value of c by substituting a coordinate into the above equation.
when x=-1, y=3,
[tex]3 = \frac{3}{2} ( - 1) + c \\ 3 = -\frac{3}{2} + c \\ c = 3 + \frac{3}{2} \\ c = 4 \frac{1}{2} [/tex]
Therefore the equation of the line is
[tex]y = \frac{3}{2} x + 4\frac{1}{2} [/tex]
