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write the equation that passes through the point (-2,-9) and has s slope of 7?

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2 Answers

Hi Marlin;
Let's use the point-slope formula...
y-y1=m(x-x1)
m is the slope.
y--9=7(x--2)
Subtracting a negative number is the same as adding a positive number...
y+9=7(x+2)
y+9=7x+14
Let's subtract 9 from both sides...
-9+y+9=7x+14-9
y=7x+5
The formula is now in the format of...
y=mx+b
This is known as slope-intercept.
m is the slope.
b is the y-intercept, the value of y when x=0.
Standard formula is...
Ax+By=C
Neither A nor B equal zero.
A is greater than zero.
y=7x+5
Let's move 7x to the left side of the equation.  It becomes negative.
-7x+y=5
Let's multiply both sides by -1 to render A greater than zero.
-1(-7x+y)=(5)(-1)
7x-y=-5
This is the equation in standard form.
OK, Marlin, we know the line has a slope of 7.  Therefore the form of the equation will be
 
y = 7x + b
 
We know that the point (-2, -9) lies on the line.  Therefore
 
-9 = (7)(-2) = b
 
b = (-9) + 14 = 5.
 
The equation of the line is
 
y = 7x + 5