Question 9)
From the line graph, taking two points
Finding the slope between (-5, 4) and (-6, 7)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(-5,\:4\right),\:\left(x_2,\:y_2\right)=\left(-6,\:7\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-5%2C%5C%3A4%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%28-6%2C%5C%3A7%5Cright%29)
![m=\frac{7-4}{-6-\left(-5\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B7-4%7D%7B-6-%5Cleft%28-5%5Cright%29%7D)
![m=-3](https://tex.z-dn.net/?f=m%3D-3)
We know that the slope-intercept of the line equation is
y = mx+b
where m is the slope and b is the y-intercept
substituting (-5, 4) and m = -3 in the slope-intercept of the line
y = mx+b
4 = -3(-5)+b
4 = 15+b
b = 4-15
b = -11
substituting b = -10 and m = -3 in the slope-intercept of the line
y = mx+b
y = -3x+(-11)
y = -3x - 11
Thus, equation is slope-intercept form will be:
y = -3x - 11
Hence, option B is true.
Question 10)
From the line graph, taking two points
Finding the slope between (4, 7) and (-8, 1)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(4,\:7\right),\:\left(x_2,\:y_2\right)=\left(-8,\:1\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%284%2C%5C%3A7%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%28-8%2C%5C%3A1%5Cright%29)
![m=\frac{1-7}{-8-4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1-7%7D%7B-8-4%7D)
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
We know that the slope-intercept of the line equation is
y = mx+b
where m is the slope and b is the y-intercept
substituting (4, 7) and m = 1/2 in the slope-intercept of the line
y = mx+b
7 = 1/2(4)+b
7 = 2+b
b = 5
substituting b = 5 and m = 1/2 in the slope-intercept of the line
y = mx+b
y = 1/2x + 5
Thus, the equation is slope-intercept form will be:
y = 1/2x + 5
Hence, option C is true.