A line that includes the points (5,t) and (4,8) has a slope of - 10. What is the value of t?

Question

 t=______

Answer 1

Hi Tat,

 

(5,t), (4,8) are points on line, slope =-10

 

slope= y₂ - y_{1 /}  x₂-x₁

 

-10 = 8-t / 4-5

 

-10 = 8-t /-1

10 = 8-t

t= -2

Answer 2

Using slope-intercept form of equation: y - 8 = -10(x - 4); y = -10x + 40 + 8 = -10x + 48, so the "b" in the form of y = mx + b is 48 (the y-intercept). Using the equation again: y - t = -10(x - 5) = -10x + 50. So, y = -10x + (50 + t). Viewing both equations, we conclude (b being the same in either equation) that 48 = 50 + t. Solving for t gives -2.

You can check this one way by re-calculating the slope using the two points now known: (4,8) and (5,-2), and get the result m = -10.

Answer 3

Use the definition of slope to find t.

 

m = (y₂ - y₁) / (x₂ - x₁) = -10

 

-10 = (8 - t) / (4 - 5) = t - 8

 

-10 = t - 8

 

t= -10 + 8 = -2

Answer 4

You can just use the slope formula to get the slope.

 

m  = (y₂-y₁) / (x₂ - x₁)

 

substituting in you get

 

-10 = (t-8)/(5-4)

-10 = t-8

-2   = t

 

Hope this helped.