A linear function has the same y-intercept as x +4y= 16 and its graph contains the point (3,5). Fill in the blank to find the y-intercept.
To find the y intercept of x+4y=16, let us convert the equation to slope-intercept form, that is, y=mx+b
To get the equation in slope-intercept form, we try to isolate y
To isolate y in x+4y=16, let us first try to get rid of x from left side
So, Let us subtract x from both sides
x-x+4y=-x+16
0+4y=-x+16
Or, 4y=-x+16
Now, to isolate y we must try to get rid of 4
So, let us divide by 4 on both sides
[tex] \frac{4}{4} y=\frac{-1}{4}x+\frac{16}{4} [/tex]
1y=[tex] \frac{-1}{4} x+\frac{4}{1} [/tex]
y=[tex] \frac{-1}{4} [/tex]x+4
If we compare y=[tex] \frac{-1}{4} [/tex]x+4 to y=mx+b
b, or y intercept=4
