Solution:
Step 1: Find the slope of the line:
Given the points (X1, Y1)=(-4,-5) and (X2, Y2)= (1,5), we have that the slope of the line that passes through the points (-4,-5) and (1,5) is:
[tex]m=\frac{Y2-Y1}{X2-X1}=\frac{5+5}{1+4}=\frac{10}{5}=2[/tex]Step 2: Write the provisional equation of the given line. If the slope of the line is m=2, we get that the provisional equation of this line is:
[tex]y\text{ =2x+b}[/tex]Step 3: Find the y-intercept b. Take any point (x,y) on the line and replace its coordinates into the above equation and then solve for b. For example, take the point (x,y)=(1,5), then we obtain:
[tex]5\text{ =2(1)+b}[/tex]this is equivalent to:
[tex]5\text{ =2+b}[/tex]solving for b, we get:
[tex]b\text{ = 5-2 = 3}[/tex]that is:
[tex]b\text{ = 3}[/tex]Step 4: Write the equation of the line. If the given line has slope m=2 and y-intercept b = 3, then its equation would be:
[tex]y\text{ =2x+}3[/tex]and in terms of x, this is equivalent to:
[tex]f(x)=2x+3[/tex]So that, we can conclude that the correct answer is:
[tex]f(x)=2x+3[/tex]