Answer:
Step-by-step explanation:
Question 8
Let the equation of a line passing through two points
and
is given by,
y = mx + b
Here, m = slope and y-intercept = b
Since, m = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
For two points (1, 4) and (5, 8),
m =
m = 1
Equation will be,
y = (1)x + b
y = x + b
Since, this line passes through (1, 4),
4 = 1 + b
b = 3
Therefore, equation of the line will be,
y = x + 3
Question 9
Let the equation is y = mx + b
m = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
For two points (2, 10) and (6, 4)
m = ![\frac{10-4}{2-6}](https://tex.z-dn.net/?f=%5Cfrac%7B10-4%7D%7B2-6%7D)
m = ![-\frac{3}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D)
By substituting the value of 'm' in the equation,
y = ![-\frac{3}{2}x+b](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7Dx%2Bb)
Since, this line passes through (2, 10)
10 = ![-\frac{3}{2}(2)+b](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D%282%29%2Bb)
b = 10 + 2
b = 12
Therefore, equation of the line will be,
![y=-\frac{3}{2}x+12](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B2%7Dx%2B12)