Answer:
The true statements are;
A. The point (0, -3) is on the line
C. The point (-6, -6) is a point on the line
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