Question

Help pls and thank you :)

Answer 1

`y=(-2)/(3) x+1`

Explanation:

Linear equations are typically organized in slope-intercept form:
`y=mx+b`. Here's what the variables mean:

y = the y-coordinate

m = the slope

x = the x=coordinate

b = the y-intercept (what y is equal to when the line crosses the y-axis)

First, we need to calculate the slope of the line (m). The slope is the
`(rise)/(run)` of the line, or in other words, the change in y over the change in x. We can find this by just looking at the graph, between the two given points. For 3 spaces the line travels to the right, it travels downward 2 spaces. Therefore, the slope of the line is
`(-2)/(3)`.

We can also calculate this using the formula
`(y_2-y_1)/(x_2-x_1)` by using two points that fall on the line,
`(x_1,y_1)` and
`(x_2,y_2)`. Here, we can use the points (-3,3) and (0,1).

`(y_2-y_1)/(x_2-x_1)\\(1-3)/(0-(-3))`

Two negatives make a positive

`=(1-3)/(0+3)\\=(-2)/(3)`

Then, we need to find the y-intercept of the line (b). We can find this by, again, looking at the graph. The line crosses the y-axis when y is equal to 1, so the y-intercept of the line is 1.

Now, we plug our calculated values back into the original equation:

`y=mx+b\\y=(-2)/(3) x+1`

I hope this helps!