(6,-3)

(10,-6)

(14,-9)

y-intercept

x-intercept

determine the intercepts of the line that passes through the following points.

x-intercept at (2, 0); y-intercept at (0, ³/₂)

Step-by-step explanation:

(a) Slope

The point-slope formula for a straight line is

y₂ - y₁ = m(x₂ - x₁)

The line goes through the points  (6, -3) and (14, -9).

-9 – (-3) = m(14 – 6)

        -6 =  -8m

        m = -⁶/₈

        m = -¾

(b) Equation of line

y = mx + b

Use the point (6, -3)

     -3 = -¾ ×6+ b

     -3 = -¹⁸/₄ + b

     -3 = -⁹/₂   + b

Add ⁹/₂ to each side

      b = -3 + ⁹/₂

      b = -⁶/₂ + ⁹/₂

      b = ³/₂

∴  y = -¾x + ³/₂

(c) y-intercept

Let x = 0.

y = -¾(0) + ³/₂ = 0 + ³/₂ = ³/₂

The y-intercept is at (0, ³/₂).

(d) x-intercept

Let y = 0.

0 = -¾x + ³/₂

Multiply each side by 4

0 = -3x + 6

Subtract 6 from each side

-6 = -3x

Divide each side by -3

x = 2

The x intercept is at (2, 0).

The insert below shows the graph with the intercepts at (2,0) and (0, ³/₂)

If K is a compact Hausdorff space, C(K) will denote the space of all real- valued, continuous functions on K. C(K) is a Banach space with the norm f∞ = maxs∈K |f(s)|.

Step-by-step explanation: