Question

a linear function has the same y-intercept as x + 4y= 8 and its graph contains the point (6,3). what is the y intercept?​

Answer 1

Answer: y-intercept = 2

Step-by-step explanation:

Slope-Intercept form of an equation is:  y = mx + b   where

• m = slope
• b = y-intercept

x + 4y = 8

     4y = -x + 8

       $y=-\dfrac{1}{4}x+\dfrac{8}{4}$

       $y=-\dfrac{1}{4}x+2$

The y-intercept (b) = 2

I am not sure why you gave a point that goes through the y-intercept because it does not relate to the question , however, I have shown below the equation of point (6, 3) that goes through b = 2.

y = mx + b

3 = m(6) + 2

1 = 6m

$\dfrac{1}{6}=m$

Equation: $y=\dfrac{1}{6}x+2$

Answer 2

Answer:

The y-intercept b = 9/2

Step-by-step explanation:

A line has equation  x + 4y = 8  or y = (-1/4)x + 2

=> The slope of this line is -1/4

Another line y = ax + b has the slope a = -1/4 and passes (6, 3)

=> 3 = (-1/4)*6 + b

=> 3 = -3/2 + b

=> b = 9/2

=> The y-intercept b = 9/2