Question

Find the equation of the linear function represented by the table below inslope-intercept form.хy-2152-56-2510-45

Answer 1

The equation of a line in intercept-slope form is given by the following expression:

y = mx + b

Where m is the slope and b is the y-intercept.

We can find the slope of the line by means of the following formula:

$m=\frac{y2-y1}{x2-x1}$

Where (x1, y1) and (x2, y2) are two points where the line passes through.

In this case, we have some points in a table, then let's use two of them, for example, take (-2, 15) and (2, -5). By replacing (-2, 15) for (x1, y1) and (2, -5) for (x2, y2) we get:

$m=\frac{-5-15}{2-(-2)}=\frac{-20}{2+2}=\frac{-20}{4}=-5$

Now that we know the value of the slope, we can replace 5 for m into the slope-intercept form to get:

y = 5x + b

By taking another pair of x and y-values from the table and, for example (6, -25), and replacing -25 for y and 6 for x, we get:

-25 = 5×6 + b

-25 = 30 + b

-25 - 30 = 30 - 30 + b

-55 = b

b= -55

Now that we know the value of the y-intercept, we can replace -55 for b into the slope-intercept equation of the line, to get:

y = 5x - 55

Then, the equation of the line that describes the given data is y = 5x - 55