Answer:
[tex]f(x)=x-5[/tex]
Step-by-step explanation:
step 1
Find the slope m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the ordered pairs
(10,5) and (2,-3)
substitute the values
[tex]m=\frac{-3-5}{2-10}[/tex]
[tex]m=\frac{-8}{-8}[/tex]
[tex]m=1[/tex]
step 2
Find the equation of the line in slope intercept form
[tex]f(x)=mx+b[/tex]
we have
[tex]m=1[/tex]
[tex]point\ (10,5)[/tex]
substitute and solve for b
[tex]5=(1)(10)+b[/tex]
[tex]5=10+b[/tex]
[tex]b=-5[/tex]
The linear function is equal to
[tex]f(x)=x-5[/tex]
The linear function with the values [tex]f(10)=5[/tex] and [tex]f(2)=-3[/tex] is [tex]f(x)=x-5[/tex].
Step-by-step explanation:
Given information:
The values of a liner function
[tex]f(10)=5[/tex]
and
[tex]f(2)=-3[/tex]
So, we can write the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\[/tex]
On, putting the values:
[tex]m=\frac{-3-5}{2-10} \\m=1[/tex]
Point (10,5)
Now ,substitute the values in the linear equation:
[tex]\text {y=mx+b}[/tex]
where, m is the slope.
[tex]5=1 \times 10 + \text b\\\text b=-5[/tex]
Now put the values to get the required linear function.
So, the linear function with the values [tex]f(10)=5[/tex] and [tex]f(2)=-3[/tex] will be [tex]f(x)=x-5\\[/tex]
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