So firstly, we have to find the y-intercept of the first equation given to us; x + 2y = 10. The easiest method of doing this is to put this equation into slope-intercept form, which is y = mx + b (m = slope, b = y-intercept.)
First step is to subtract x on both sides of that equation: 2y = -x + 10
Next, divide 2 on both sides of the equation, and your slope-intercept form is: y = -1/2x + 5.
Looking at that equation, it appears that our y-intercept is (0,5).
Next, the slope formula is [tex] \frac{y_2-y_1}{x_2-x_1} [/tex] . For this, I'll be using points (9,7) and (0,5). [tex] \frac{7-5}{9-0}=\frac{2}{9} [/tex]
In short, the slope is 2/9, or B.
