Question

Part A

Answer 1

Answer:

a) b = -5

b) slope = 3/2

Explanation:

a) The equation of a line is given as y = mx + b, where m is the slope of the line and b is the intercept on the y axis.

Given that y = 3x + b and it passes through the point (2, 1). Hence when x = 2, y = 1. Therefore, substituting for x and y:

1 = 3(2) + b

1 = 6 + b

b = 1 - 6

b = -5

b) The equation of a line passing through two points ($x_1,y_1$) and $x_2,y_2$ is given by:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of the line passing through the two points (0,3) and (4,9) is:

$y-3=\frac{9-3}{4-0}(x-0)\\ \\y-3=\frac{3}{2}x\\ \\y = \frac{3}{2}x+3$

Comparing y = (3/2)x + 3 with y = mx + b, the slope (m) is 3/2