Question

Part C

Answer 1

a = 1, b =14 and y-coordinate is 6 when x = 0.

Solution:

Let us first write the equation of a line.

Take the points are (2, 2) and (6, 10).

Slope of the line:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{10-2}{6-2}$

$m=\frac{8}{4}$

m = 2

Point-slope formula:

$y-y_1=m(x-x_1)$

y - 10 = 2(x - 2)

y - 10 = 2x - 4

Add 10 on both sides,we get

y = 2x + 6

Equation of a line is y = 2x + 6.

To find (a, 8), substitute x = a and y = 8 in the equation,

8 = 2a + 6

Subtract 6 from both sides, we get

2 = 2a

a = 1

To find (4, b), substitute x = 4 and y = b in the equation,

b = 2(4) + 6

b = 8 + 6

b = 14

Substitute x = o in the equation.

y = 2(0) + 6

y = 6

The y-coordinate is 6 when x = 0.