Question

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.
y-intercept:(0,___)

Answer 1

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

$\frac{4}{4} y=\frac{-1}{4}x+\frac{16}{4}$

1y=$\frac{-1}{4} x+\frac{4}{1}$

y=$\frac{-1}{4}$x+4

If we compare y=$\frac{-1}{4}$x+4 to y=mx+b

b, or y intercept=4