Question

Graph the function.

Answer 1

Answer:

$\displaystyle{y=-3x-1}$

Step-by-step explanation:

I have two methods: standard-learning which will explain overall mathematically - basically formula, etc. - while the other one trick-tips method will rely on choices rather mathematical calculations but with explanation on why and how.

Standard-Learning

First, let’s pick two points that are integers since they are easily to be found via graphs. We see that (-1,2) and (0,-1) is a part of the graph so now we finally have picked two points for our calculations.

When we have finally picked two points, we will be using them for slope calculation. This part is crucial for finding an equation of a line because a line has to contain slope in its equation.

To calculate the slope, we use rise over run formula which is:

$\displaystyle{\dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}}$

Note that $\displaystyle{\Delta}$ is delta - in both mathematic and physics, it means changes in.

So, we will be using those two points that we have picked to substitute in the slope formula. Let’s determine that $\displaystyle{(x_2,y_2)=(-1,2)}$ and $\displaystyle{(x_1,y_1)=(0,-1)}$.

Therefore, our slope will be:

$\displaystyle{m=\dfrac{2-(-1)}{-1-0}}\\\\\displaystyle{m=\dfrac{2+1}{-1}}\\\\\displaystyle{m=-3}$

Next, find the y-intercept. From the graph, we see that the graph intercepts at (0,-1) which is y-intercept so we will only use y-value. Hence, b = -1.

From the slope-intercept form:

$\displaystyle{y=mx+b}$

Substitute m (slope) = -3 and b (y-intercept) = -1. Hence, the equation of line is:

$\displaystyle{y=-3x-1}$

Fast Way (Trick-Tips)

Relying on choices and knowledge of graph, notice that there are slopes of 3 and -3.

Keep in mind that if slope is negative, it will decrease down and if slope is positive, it will increase up.

Therefore, cut off all choices with positive slopes which are 1 and 3. We are now left with 2 and 4.

Next, look at the graph and tell its y-intercept. It intercepts y at y = -1 so we take value of -1.

So choice 4 is cut off and now we have choice 2 as the answer.

Learn More:

brainly.com/question/27514958 - Find the line equation with given points