Question

13

Answer 1

Answer:

The required equation is: $\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}$

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 $y=mx+b$

where m is slope and b is y-intercept.

Finding Slope

We can used the slope formula to find slope: $Slope=\frac{y_2-y_1}{x_2-x_1}$

From the table we have: $x_1=3, y_1=-5, x_2=7, y_2=-2$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}$

So, we get slope $m=\frac{3}{4}$

Now, finding y-intercept

Using the slope $m=\frac{3}{4}$ and point (3,-5) we can find y-intercept

$y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}$

The y-intercept is $b=\frac{-29}{4}$

So, the equation having slope $m=\frac{3}{4}$ and y-intercept $b=\frac{-29}{4}$ will be:

$y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}$

The required equation is: $\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}$