Read each question carefully and make sure you show w 1. Which statements are true about the line shown on the graph
graphi
Select all that apply.
A. The point (0, -3) is on the line.
107
B
6
B. The graph represents the equation 4x + 8y = -24
C. The point (-6, -6) is on the line.
D. The point (0, -4) is on the line.
4
2
10 8 8 4
20
2+
2
16 8 10
E. The point (-6, 0) is on the line.
4
F. The graph represents the equation-4x + 8y = 24.
6
8
10+

The true statements are;

A. The point (0, -3) is on the line

C. The point (-6, -6) is a point on the line

Step-by-step explanation:

The question relates to the finding of the equation of a straight line graph

The x-intercept of the graph is (6, 0) and the graph passes through the point (2, -2)

Therefore, the slope of the graph is m = (-2 - 0)/(2 - 6) = 0.5

The equation of the graph in point and slope form is given as follows;

y - 0 = 0.5 × (x - 6)

∴ y = 0.5·x - 3

Therefore, the equation of the graph in slope and intercept form, y = m·x + c is also y = 0.5·x - 3

A. The y-intercept of the graph is (0, -3), therefore, the point (0, -3) is on the line

B. The equation of the graph, y = 0.5·x - 3, can be written as follows;

8·y = 8 ×0.5·x - 8 × 3 = 4·x - 24

∴ 8·y - 4·x = -24

C. When y = -6, 'x' is given as follows;

 y = 0.5·x - 3

-6 = 0.5·x - 3

0.5·x = -6 + 3 = -3

x = -3/0.5 = -6

x = -6

Therefore, when y = -6, x = -6, and (-6, -6) is a point on the line

D. When x = 0, 'y', is given as follows;

y = 0.5·x - 3

When x = 0, y = 0.5 × (0) - 3 = -3

Therefore the point (0, -3) is on the line and the point (0, -4) is not on the line

E. The point (-6, 0) represent an x-intercept of a line graph, however the x-intercept on the given line is (6, 0) and when y = 0 on the line, x = 6

Therefore, the point (-6, 0) is not on the line

F. The equation of the graph is 8·y - 4·x = -24, therefore, - 4·x + 8·y = 24 does not represent the equation of the graph