Mathematics: What is the equation of this graphed line? please answer in slope-intercept form

What is the equation of this graphed line? please

Ответ:

miguel454545

27.01.2022

Mathematics

$y=-\frac{1}{3}x -5$

Step-by-step explanation:

Slope-intercept form is y=mx+b , so that's the equation you'll be plugging your values into.

To find the slope of a line, you only need two points, which this graph gives you. (-6, -3) and (6, -7)

Slope, or m, can be found by using $\frac{y_2-y_1}{x_2-x_1}$ . Now you just plug in your points into the formula, giving you $\frac{(-7)-(-3)}{(6)-(-6)} =\frac{-4}{12} =\frac{-1}{3}$ .

Since you don't have an intercept, choose one of the two given points to plug into the equation y-y_1=m(x-x_1) .

* It doesn't matter which point you use, both will give you a correct answer.

Let's use (-6, -3).

Since you now have a y_1, x_1, and your , all you need to do is plug them in.

$y-y_1=m(x-x_1)\\y-(-3)=-\frac{1}{3}(x-(-6))\\y+3=-\frac{1}{3} (x+6)\\y+3=-\frac{1}{3} x-2\\y=-\frac{1}{3} x-5$

If you want, you can plug in points just to confirm that this is the right equation. The simplest way to find out is by making x=0, which gives you a y value of -5. You can see on the graph that the line passes through -5 on the y-axis when x=0, so the equation is valid.