ANSWER
The y-intercept is -1
EXPLANATION
First we have to find the slope of the line and then find the y-intercept from the slope-intercept form of its equation:
[tex]y=mx+b[/tex]m is the slope and b is the y-intercept.
The slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]For this line, the slope is:
[tex]m=\frac{5-(-9)}{3-(-4)}=\frac{5+9}{3+4}=\frac{14}{7}=2[/tex]For now we have:
[tex]y=2x+b[/tex]To find the y-intercept, b, we have to replace x and y with the coordinates of one of the given points and solve for b:
[tex]\begin{gathered} 5=2\cdot3+b \\ 5=6+b \\ b=5-6 \\ b=-1 \end{gathered}[/tex]