Question

6. Two linear equations are shown in the graph.

*(0.6)
(6,5),
COD).
(6.0)
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What are the coordinates of the point where the two lines intersect?
A. (-2, 3)
B. (3, 0)
C.(-3.3)
D. (3, 3)
Mark for review (Will be highlighted on the review page)
Alaviation

Answer 1

D.(3, 3)

Explanation:

The equation of a straight line is given as:

y = mx + c;

where x, y are variables, m is the slope of the line, c is the y intercept.

From the graph, we can see that line 1 passes through (6,0) and (0,6).

The equation of line 1 is given as:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\y-0=(6-0)/(0-6) (x-6)\\\\y=-x + 6\ \ \ (1)`

Line 2 passes through (6, 5) and (0, 1)

The equation of line 2 is given as:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\y-5=(1-5)/(0-6) (x-6)\\\\y=(2)/(3)x + 1\ \ \ (2)`

To get the coordinates of the intersection of the two lines, we solve equation 1 and 2 simultaneously using a calculator. This gives:

x = 3, y = 3

Therefore the two lines meet at (3, 3)