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.