Respuesta :
[tex]\huge\boxed{\bold{f(x)=x+7}}[/tex]
Linear function
The graph of a linear function is a straight line. The directional equation of a linear function in slope-intercept form is:
[tex]\huge\boxed{f(x)=mx+b}[/tex]
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:
[tex]\boxed{\bold{m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}}}[/tex]
[tex]m = \dfrac{17-12}{10-5}=\dfrac{5}{5}=\underline{\bold{1}}[/tex]
Now we can use one of the points to find the y-intercept. Let's do that for [tex]f(5)=12[/tex]:
[tex]\begin{array}{lll}1\cdot 5+b=12\\\\5+b=12&|&-5\\\\\underline{\bold{b=7}}\end{array}[/tex]
Therefore, the linear function in slope-intercept form is:
[tex]\boxed{f(x)=x+7}[/tex]
