Equation of the line: [tex]g(x)=x-2[/tex], value of [tex]g(3)=1[/tex]
Step-by-step explanation:
For the function g(x) in this problem, we have the following data:
- at [tex]x_1=-3[/tex], the value of the function is [tex]y_1=-5[/tex]
- at [tex]x_2=5[/tex], the value of the function is [tex]y_2=3[/tex]
Therefore, we can find the slope of the line by using:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{5-(-3)}=\frac{8}{8}=1[/tex]
Now we can find the equation of the line by using
[tex]y-y_1 = m(x-x_1)[/tex]
By substituting [tex]m,x_1,y_1[/tex] we find:
[tex]y-(-5)=1(x-(-3))\\y+5=x+3[/tex]
And re-arranging into slope-intercept form,
[tex]y=x-2[/tex]
And now we can also find the value of g(3) by substituting x = 3:
[tex]g(3)=x-2=3-2=1[/tex]
Learn more about lines:
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