Photo AI

The line $k$ passes through the points (0, 2) and (4, 0) - Leaving Cert Mathematics - Question 11 - 2010

Question 11

The line $k$ passes through the points (0, 2) and (4, 0). (i) Find the equation of $k$. (ii) Write down the three inequalities which define the shaded region in th... show full transcript

Worked Solution & Example Answer:The line $k$ passes through the points (0, 2) and (4, 0) - Leaving Cert Mathematics - Question 11 - 2010

Step 1

Find the equation of $k$

96%

114 rated

Answer

To find the equation of the line $k$ , we first determine the slope (m) using the formula:

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

where the points are (0, 2) and (4, 0).

Substituting the coordinates:

$m = \frac{0 - 2}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}$

Using the point-slope form of the equation, $y - y_1 = m(x - x_1)$ , we can choose point (0, 2):

$y - 2 = -\frac{1}{2}(x - 0)$

Simplifying gives us:

$y = -\frac{1}{2}x + 2$

Thus, the equation of line $k$ is:

$y = -\frac{1}{2}x + 2$

Step 2

Write down the three inequalities which define the shaded region in the diagram

99%

104 rated

Answer

The shaded region is defined by the following inequalities:

From the line $k$ : $y \leq -\frac{1}{2}x + 2$
From the horizontal line along the x-axis: $y \geq 0$
From the vertical line along the line $x = 4$ : $x \leq 4$

These inequalities collectively define the area that is shaded in the diagram.

Join the Leaving Cert students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;