Answer:
The required equation is: [tex]\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}[/tex]
Step-by-step explanation:
We need to find equation from the table given
x f(x)
3 -5
7 -2
11 1
15 4
We can write equation in the form of [tex]y=mx+b[/tex]
where m is slope and b is y-intercept.
Finding Slope
We can used the slope formula to find slope: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table we have: [tex]x_1=3, y_1=-5, x_2=7, y_2=-2[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}[/tex]
So, we get slope [tex]m=\frac{3}{4}[/tex]
Now, finding y-intercept
Using the slope [tex]m=\frac{3}{4}[/tex] and point (3,-5) we can find y-intercept
[tex]y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}[/tex]
The y-intercept is [tex]b=\frac{-29}{4}[/tex]
So, the equation having slope [tex]m=\frac{3}{4}[/tex] and y-intercept [tex]b=\frac{-29}{4}[/tex] will be:
[tex]y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}[/tex]
The required equation is: [tex]\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}[/tex]
