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

(3,3)

Explanation:

Linear equations of lines are given in the form:

y = mx + b;

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

From the graph, we can see that line 1 passes through (0,6) and (6,0) while line 2 passes through (0, 1) and (6, 5).

The equation of line 1 is given as:

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

The equation of line 2 is given as:

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

Solving equation 1 and 2 simultaneously by subtracting equation 1 from 2 gives:

(5/3)x - 5 = 0

(5/3)x = 5

x = 3

Put x = 3 in equation 1:

y = -3 + 6 = 3

Therefore the two lines meet at (3, 3).