Question

for linear function f, f (10)=17, f(5)=12. Complete the function in slope-intercept form?

Answer 1

$\huge\boxed{\bold{f(x)=x+7}}$

Linear function

The graph of a linear function is a straight line. The directional equation of a linear function in slope-intercept form is:

$\huge\boxed{f(x)=mx+b}$

Where:

• f(x) represents the output (or dependent variable) of the function for a given input
• x represents the input (or independent variable) of the function.
• m represents the slope of the line, which determines its steepness or inclination.
• b represents the y-intercept, which is the point where the line intersects the y-axis.

Solution:

Let's find the m using point-slope formula:

     $\boxed{\bold{m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}}}$

     $m = \dfrac{17-12}{10-5}=\dfrac{5}{5}=\underline{\bold{1}}$

Now we can use one of the points to find the y-intercept. Let's do that for $f(5)=12$:

     $\begin{array}{lll}1\cdot 5+b=12\\\\5+b=12&|&-5\\\\\underline{\bold{b=7}}\end{array}$

Therefore, the linear function in slope-intercept form is:

     $\boxed{f(x)=x+7}$