Question

10 The equation of a linear graph is 4y - 2x + 8 = 20. a)Show that (-6, 0) is on the line. b)Show that (4, 5) is on the line. c)Make y the subject of the equation. d)Write the gradient and the y-intercept of the line.

Answer 1

Відповідь:

a) To show that (-6, 0) is on the line, we substitute x = -6 and y = 0 into the equation and check if it holds true:

4y - 2x + 8 = 20

4(0) - 2(-6) + 8 = 20

12 + 8 = 20

20 = 20

Since the equation holds true, (-6, 0) is on the line.

b) Similarly, to show that (4, 5) is on the line, we substitute x = 4 and y = 5 into the equation:

4y - 2x + 8 = 20

4(5) - 2(4) + 8 = 20

20 - 8 + 8 = 20

20 = 20

Since the equation holds true, (4, 5) is on the line.

c) To make y the subject of the equation, we isolate the term with y on one side:

4y - 2x + 8 = 20

4y = 2x + 12

y = (2/4)x + 3/2

Simplifying, we get:

y = (1/2)x + 3/2

d) The equation is in the form y = mx + c, where m is the gradient and c is the y-intercept. Therefore, the gradient is 1/2 and the y-intercept is 3/2.

Answer 2

To solve this problem, we'll follow the given steps:

a) Show that (-6, 0) is on the line:

Substitute the x and y values of (-6, 0) into the equation and check if it satisfies the equation.

4y - 2x + 8 = 20

4(0) - 2(-6) + 8 = 20

0 + 12 + 8 = 20

20 = 20

Since both sides of the equation are equal, (-6, 0) satisfies the equation, which means it is on the line.

b) Show that (4, 5) is on the line:

Substitute the x and y values of (4, 5) into the equation and check if it satisfies the equation.

4y - 2x + 8 = 20

4(5) - 2(4) + 8 = 20

20 - 8 + 8 = 20

20 = 20

Similarly, since both sides of the equation are equal, (4, 5) satisfies the equation and is on the line.

c) Make y the subject of the equation:

To make y the subject of the equation, we need to isolate it on one side of the equation.

4y - 2x + 8 = 20

4y = 2x - 12

y = (2x - 12) / 4

Simplifying further:

y = (1/2)x - 3

Now y is the subject of the equation.

d) Write the gradient and the y-intercept of the line:

From the equation in part c, we can see that the coefficient of x, which is 1/2, represents the gradient (slope) of the line. The y-intercept is the constant term, which is -3.

Therefore, the gradient of the line is 1/2, and the y-intercept is -3.