Answer
Find out the value of x .
To proof
SAS congurence property
In this property two sides and one angle of the two triangles are equal.
in the Δ ADC and ΔBDC
(1) CD = CD (common side of both the triangle)
(2) ∠CDA = ∠ CDB = 90 °
( ∠CDA +∠ CDB = 180 ° (Linear pair)
as given in the diagram
∠CDA = 90°
∠ CDB = 180 ° - 90°
∠ CDB = 90°)
(3) AD = DB (as shown in the diagram)
Δ ADC ≅ ΔBDC
by using the SAS congurence property .
AC = BC
(Corresponding sides of the congurent triangle)
As given
the length of AC is 2x and the length of BC is 3x - 5 .
2x = 3x - 5
3x -2x =5
x = 5
The value of x is 5 .
Hence proved
Given:
A straight-line graph has gradient 4 and crosses the y axis at (0, −3).
To find:
The equation of the given graph.
Solution:
The slope intercept form of a line is:
...(i)
Where, m is the slope of the line and b is the y-intercept.
A straight-line graph has gradient 4. It means the slope of the line is 4.

Line crosses the y axis at (0, −3). So, y-intercept is -3.

Putting m=4 and b=-3 in (i), we get


Therefore, the equation of the given line graph is
.