Answer:
Question No 4
The equation will be: ![y=-\frac{1}{2}x+11](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B11)
Option B is correct answer.
Question No 5
The equation will be: ![y=\frac{3}{4}x+4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B4%7Dx%2B4)
Option A is correct answer.
Step-by-step explanation:
Question 4
The option equations are in slope intercept forms, so we will write equation in slope intercept form.
The general equation of slope intercept form is:
where m is slope and b is y-intercept
Finding Slope:
Using the point (2,10) and (4,9) we can find slope
The formula used is: ![Slope=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Putting values and finding slope:
![Slope=\frac{9-10}{4-2}\\Slope=-\frac{1}{2}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7B9-10%7D%7B4-2%7D%5C%5CSlope%3D-%5Cfrac%7B1%7D%7B2%7D)
So, we get slope m = - 1/2
Finding y-intercept
Using point (2,10) and slope m =1/2 we can find y-intercept
![y=mx+b\\10=-\frac{1}{2}(2)+b\\10=-1+b\\b=10+1\\b=11](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C10%3D-%5Cfrac%7B1%7D%7B2%7D%282%29%2Bb%5C%5C10%3D-1%2Bb%5C%5Cb%3D10%2B1%5C%5Cb%3D11)
So, equation will be:
![y=mx+b\\y=-\frac{1}{2}x+11](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B11)
Option B is correct answer.
Question 5
The option equations are in slope intercept forms, so we will write equation in slope intercept form.
The general equation of slope intercept form is:
where m is slope and b is y-intercept
Finding Slope:
Using the point (0,4) and (4,7) from the graph we can find slope
The formula used is: ![Slope=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Putting values and finding slope:
![Slope=\frac{7-4}{4-0}\\Slope=\frac{3}{4}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7B7-4%7D%7B4-0%7D%5C%5CSlope%3D%5Cfrac%7B3%7D%7B4%7D)
So, we get slope m = 3/4
Finding y-intercept
Using point (0.4) and slope m = 3/4 we can find y-intercept
![y=mx+b\\4=\frac{3}{4}(0)+b\\4=0+b\\b=4](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C4%3D%5Cfrac%7B3%7D%7B4%7D%280%29%2Bb%5C%5C4%3D0%2Bb%5C%5Cb%3D4)
So, equation will be:
![y=mx+b\\y=\frac{3}{4}x+4](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D%5Cfrac%7B3%7D%7B4%7Dx%2B4)
Option A is correct answer.