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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
Answer:
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Step-by-step explanation:
You treat inequality questions just like normal equation with an equal sign. You only have to worry about the inequality when you do the shading part.
Your first goal is to solve for y, which I did at the top.
And remember that when you divide/multiply by a negative number you have to flip the inequality sign.
So the first equation is already in term of y. (y < 2x + 4)
So you only have to solve for y for -3x - 2y ≥ 6.
I solved that and got y ≤ -3/2x - 3.
Now you have 2 equations. y < 2x + 4 and y ≤ -3/2x - 3
First you gotta treat it like a normal equation and graph them.
So i graphed y = 2x + 4 and y = -3/2x - 3. I assume you already know how do do that.
btw. < and > have dotted lines, while ≤ and ≥ have solid lines.
Now for the shading, you gotta look at the inequality sign.
y < 2x + 4 has a less than sign, so you have to shade everything underneath the line you graphed.
y ≤ -3/2x - 3 is also less than, so you have to shade everything underneath that line as well.
So in the future, you you get a > or ≥ then you have to shade above the graph.
