Question

Find the slope of linear functions by either identifying a pattern or calculating slope. Then find the y-intercept. Use both slope and y-intercept to write the equation of the line.



Explain this answer don’t just say the answer how would I be able to solve this

Answer 1

Answer:

Slope: -1

y-intercept: -3

Equation: f(x) = -x - 3

Step-by-step explanation:

To write the equation in y = mx + b form, we need to know the slope(m) and y-intercept(b) of the equation.

There are two ways to find the slope. The first and easiest way for this problem is to identify a pattern in the table. As x increases by 1, f(x) decreases by 1. This means that our slope is -1, as slope is the same thing as the change in f(x) over the change in x.

The other method of finding the slope is to take two points from the table (in this example I'll use points (1, -4) and (2, -5)) and input them into the slope formula: $\frac{y2-y1}{x2-x1}$

$\frac{-5 - (-4)}{2 -1}$

Solve:

-5 - (-4) = -5 + 4 = -1

2 - 1 = 1

-1/1 = -1

The slope is -1.

Now that we know the slope, we can input the value of the slope into the equation f(x) = mx + b:

f(x) = -1x + b

To find the y-intercept, take a point from the table, for example point (1, -4) and input that point into the equation:

-4 = -1(1) + b

Now we can solve for b:

-4 = -1 + b

Add 1 to both sides of the equation to isolate the b:

-4 + 1 = -1 + 1 + b

-3 = b

The y-intercept is -3.

Now that we have the values for both the slope and the y-intercept, we can input them into our equation and get our answer:

f(x) = -x - 3

We can make sure this equation is correct by using a point from the table, for example point (2, -5) and input it into the equation:

-5 = -1(2) - 3

-5 = -2 - 3

-5 = -5

The values came out to be equal, which means that our equation is correct.

Hope this helps :)