Question

Please write an equation for both i need help bad!

Answer 1

Answer:

$\huge\boxed{1.\ y=-\frac{1}{2}x+1}$

$\huge\boxed{2. \ y=\frac{3}{2}x}$

Step-by-step explanation:

In order to find the equation for these graphs, we have to note what forms a line.

The slope: Which is just the rise of the line over the run - how much it increases in y over how much it increases in x.

The y-intercept: Where does the graph intersect the y-axis?

Fortunately, there's a type of formula commonly used that includes both of these - slope-intercept form. It is written in the form $y=mx+b$, where m is the slope and b is the y-intercept.

For number 1:

We can see that the graph intersects the y-axis at 1. So the y-intercept is 1, aka b = 1.

We can also see that for every 1 decrease in y, x increases by 2. This is where the two dots come in useful. This means our change in y is -1 and our change in x is 2. Since slope is rise over run, we can divide it.

$-1 \div 2 = -\frac{1}{2}$

Now that we know the slope and the y-intercept, we can plug these values into $y=mx+b$.

$y=-\frac{1}{2}x+1$

For Number 2:

Same logic applies. The graph intersects the y-axis at 0, so b = 0, aka we don't need to include that term in the end equation.

We can see that when x increases by 2, y increases by 3. Since the slope is rise over run, the slope is $\frac{3}{2}$.

$y=mx+b$

$y=\frac{3}{2}x$

Hope this helped!