Question

a linear function has the same y-intercept as x + 4y equals 16 and it's graph contains the point (4,5). Find the slope of the linear function. ​

Answer 1

Answer:  $\bold{\text{Slope (m)}=\dfrac{1}{4}}$

Explanation:

A linear equation is of the form: y = mx + b   where

• m is the slope
• b is the y-intercept (where it crosses the y-axis)

x + 4y = 16

     4y = -x + 16

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

       $y=-\dfrac{1}{4}x+4$

The y-intercept (b) = 4

Next, find the slope given point (4, 5) and b = 4

$y=mx+b\\\\5=m(4)+4\\\\1=4m\\\\\dfrac{1}{4}=m\\\\\\\\\large\boxed{Slope (m)=\dfrac{1}{4}}$