Answer:
Step-by-step explanation:
Question 8
Let the equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
y = mx + b
Here, m = slope and y-intercept = b
Since, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For two points (1, 4) and (5, 8),
m = [tex]\frac{8-4}{5-1}[/tex]
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 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For two points (2, 10) and (6, 4)
m = [tex]\frac{10-4}{2-6}[/tex]
m = [tex]-\frac{3}{2}[/tex]
By substituting the value of 'm' in the equation,
y = [tex]-\frac{3}{2}x+b[/tex]
Since, this line passes through (2, 10)
10 = [tex]-\frac{3}{2}(2)+b[/tex]
b = 10 + 2
b = 12
Therefore, equation of the line will be,
[tex]y=-\frac{3}{2}x+12[/tex]
