Answer:
[tex]\displaystyle y = \frac{1}{2}x + 5[/tex]
Step-by-step explanation:
Equation of a Line
The point-slope form of the equation of a line is:
y - k = m ( x - h )
Where m is the slope and (h,k) is a point through which the line passes.
Suppose a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We'll use the points (-4,3) and (2,6), thus:
[tex]\displaystyle m=\frac{6-3}{2+4}=\frac{3}{6}=\frac{1}{2}[/tex]
Now we use the point-slope form using the point (2,6):
[tex]\displaystyle y - 6 = \frac{1}{2}( x - 2 )[/tex]
Operating:
[tex]\displaystyle y - 6 = \frac{1}{2}x - 1[/tex]
[tex]\displaystyle y = \frac{1}{2}x - 1 + 6[/tex]
[tex]\boxed{\displaystyle y = \frac{1}{2}x + 5}[/tex]
