Question

Use the table below to find the equation for the line. If a value is not an integer type it as a decimal rounded to the nearest hundredth. Do not put any spaces between your characters.x051015g(x)5-10-25-40The equation for the line is g(x)= Answer

Answer 1

To be able to determine the equation of the line, we need to have a y-intercept and its slope.

The y-intercept is the value of y when x = 0. In the table that we have, when x = 0, g(x) = 5, hence, our y-intercept is 5.

Next, let's determine the slope. To determine the slope, we need two points and the formula below:

`\text{slope}=(y_2-y_1)/(x_2-x_1)`

Let's make use of the points (0, 5) and (5, -10). These will be our (x₁, y₁) and (x₂, y₂). Let's plug these values to the slope formula above.

`\text{slope}=(-10-5)/(5-0)=-(15)/(5)=-3`

Hence, the slope of the line is -3.

Now that we have slope = -3 and y-intercept = 5, we can now use the slope-intercept equation of the line that is:

`y=mx+b`

where m = slope and b = y-intercept.

`y=-3x+5`

Answer: The equation of the line is g(x) = -3x + 5.

Note that g(x) = y.