Answer:
j = 0
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]\large\boxed{y=mx+b}[/tex]
where:
- m is the slope.
- b is the y-intercept.
Given:
- Slope = -¹/₄
- Point = (8, 3)
Substitute the given slope and point into the formula and solve for b:
[tex]\begin{aligned}y & = mx+b\\\implies 3 & = -\dfrac{1}{4}(8)+b\\3 & = -2+b\\3+2&=-2+b+2\\5&=b\\\implies b & =5\end{aligned}[/tex]
Substitute the given slope and found value of b into the formula to create an equation for the line:
[tex]\boxed{y=-\dfrac{1}{4}x+5}[/tex]
Substitute the point (j, 5) into the equation and solve for j:
[tex]\begin{aligned}y&=-\dfrac{1}{4}x+5\\\implies 5&=-\dfrac{1}{4}j+5\\5-5&=-\dfrac{1}{4}j+5-5\\0&=-\dfrac{1}{4}j\\\implies j&=0\end{aligned}[/tex]
Solution
Therefore, the value of j is 0.
