The first equation, 8x - 9y = - 23
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = ( 
, 3) and (x₂, y₂ ) = (- 4, - 1 )
m = 
= (- 4)/- 
= 
partial equation is y = x + c
to find c substitute either of the 2 points into the partial equation
using (- 4, - 1 ), then
- 1 = - 
+ c ⇒ c = 
y = x + ← in slope- intercept form
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
rearrange the slope- intercept equation into this form
multiply through by 9
9y = 8x + 23 ( subtract 9y and 23 from both sides )
8x - 9y = - 23 in standard form
B) y = -2x
when x = a
y = -2a
when x= 2a
y = -2(2a) = -4a
the commutative property was used
The value of y is 50
The angle measurement of angle AOB is 100°
<h3>Circle Geometry </h3>
From the question, we are to determine the value of y and the measure of angle AOB
From one the circle theorems, we have that
Angles in the <u>same segment</u> are equal
In the given diagram, x° and y° are angles in the same segment
∴ x° = y°
From the given information,
x = 50
∴ y = 50
Hence, the value of y is 50
Also, from another circle theorem,
Angle at the <u>center</u> is twice the angle at the <u>circumference</u>
∴ ∠AOB = 2x° = 2y°
Then,
∠AOB = 2×50°
∠AOB = 100°
Hence, the angle measurement of angle AOB is 100°
Learn more on Circle Geometry here: brainly.com/question/17074363
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