Question

The points (8, 3) and (j, 5) fall on a line with a slope of -1/4. What is the value of j? help me ASAP ​

Answer 1

j = 0

Explanation:

Slope-intercept form of a linear equation:

`\large\boxed{y=mx+b}`

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:

`\begin{aligned}y & = mx+b\\\implies 3 & = -(1)/(4)(8)+b\\3 & = -2+b\\3+2&=-2+b+2\\5&=b\\\implies b & =5\end{aligned}`

Substitute the given slope and found value of b into the formula to create an equation for the line:

`\boxed{y=-(1)/(4)x+5}`

Substitute the point (j, 5) into the equation and solve for j:

`\begin{aligned}y&=-(1)/(4)x+5\\\implies 5&=-(1)/(4)j+5\\5-5&=-(1)/(4)j+5-5\\0&=-(1)/(4)j\\\implies j&=0\end{aligned}`

Solution

Therefore, the value of j is 0.

Answer 2

Answer: j = 0

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Work Shown:

m = slope

m = (y2 - y1)/(x2 - x1)

m = (5 - 3)/(j - 8)

m = 2/(j - 8)

Plug in the given slope of -1/4 and solve for j

m = 2/(j - 8)

-1/4 = 2/(j - 8)

-1*(j-8) = 4*2

-j + 8 = 8

-j = 8-8

-j = 0

j = 0

The slope through (8,3) and (0,5) is -1/4

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Check:

m = (y2 - y1)/(x2 - x1)

m = (5-3)/(0-8)

m = 2/(-8)

m = -1/4

The answer is confirmed.