Answer:
Question 4: ![y=\displaystyle -\frac{4}{5}x](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%20-%5Cfrac%7B4%7D%7B5%7Dx)
Question 5: ![y=-5x-3](https://tex.z-dn.net/?f=y%3D-5x-3)
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form:
where <em>m</em> is the slope of the line and <em>b</em> is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).
<u>Question 4</u>
<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>
where two points that pass through the line are
and ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:
![\displaystyle m=\frac{-4-4}{5-(-5)}\\\\\displaystyle m=\frac{-4-4}{5+5}\\\\\displaystyle m=\frac{-8}{10}\\\\\displaystyle m=-\frac{4}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B-4-4%7D%7B5-%28-5%29%7D%5C%5C%5C%5C%5Cdisplaystyle%20m%3D%5Cfrac%7B-4-4%7D%7B5%2B5%7D%5C%5C%5C%5C%5Cdisplaystyle%20m%3D%5Cfrac%7B-8%7D%7B10%7D%5C%5C%5C%5C%5Cdisplaystyle%20m%3D-%5Cfrac%7B4%7D%7B5%7D)
Therefore, the slope of the line is
. Plug this into
as the slope (<em>m</em>):
![y=\displaystyle -\frac{4}{5}x+b](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%20-%5Cfrac%7B4%7D%7B5%7Dx%2Bb)
<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>
On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (<em>b</em>) is 0. Plug this into
:
![y=\displaystyle -\frac{4}{5}x+0\\\\y=\displaystyle -\frac{4}{5}x](https://tex.z-dn.net/?f=y%3D%5Cdisplaystyle%20-%5Cfrac%7B4%7D%7B5%7Dx%2B0%5C%5C%5C%5Cy%3D%5Cdisplaystyle%20-%5Cfrac%7B4%7D%7B5%7Dx)
<u>Question 5</u>
<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>
![\displaystyle m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:
![\displaystyle m=\frac{-3-2}{0-(-1)}\\\\\displaystyle m=\frac{-3-2}{0+1}\\\\\displaystyle m=\frac{-5}{1}\\\\m=-5](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B-3-2%7D%7B0-%28-1%29%7D%5C%5C%5C%5C%5Cdisplaystyle%20m%3D%5Cfrac%7B-3-2%7D%7B0%2B1%7D%5C%5C%5C%5C%5Cdisplaystyle%20m%3D%5Cfrac%7B-5%7D%7B1%7D%5C%5C%5C%5Cm%3D-5)
Therefore, the slope is -5. Plug this into
:
![y=-5x+b](https://tex.z-dn.net/?f=y%3D-5x%2Bb)
<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>
On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (<em>b</em>) is -3. Plug this into
:
![y=-5x+(-3)\\y=-5x-3](https://tex.z-dn.net/?f=y%3D-5x%2B%28-3%29%5C%5Cy%3D-5x-3)
I hope this helps!