Explain in words how to write an equation y=2/3x-4 passing through the point (-2,-5). write your answer in standard form.

Question

cannot figure out how to write it in word to solve

Answer 1

Explain in words:  Y=mX+b  is the slope-intercept form where:

 

m=slope, b=Y-intercept   (NOTE: Y-intercept occurs when X=0)

 

You gave an equation in this form:  Y= 2/3X-4

 

Therefore, (m=2/3) & (Y-intercept=-4)

 

However - this line DOES NOT PASS THROUGH (-2,-5).  You can see this is true by plugging in (X=-2) into the equation.  When you do this, Y=(-4/3 -4) = -16/3  or -5 1/3 (ie Y does not equal -5).

Answer 2

Hi Phyllis;

y=(2/3)x-4

The equation is in slope-intercept form...

y=mx+b

m is the slope, the change-of-y divided by the change-of-x, also known as rise-over-run.  In this equation, it is 2/3.  The line rises two units for every three units it shifts to the right.  The line descends two units for every three units it shift to the left.

b is the y-intercept, the value of y when x=0.  It is the point at which the line crosses the y-axis.  In this equation, such point is (0,-4).

Standard form is...

Ax+By=C, Neither A nor B equal zero, and A is greater than zero.

y=(2/3)x-4

Let's subtract (2/3)x from both sides...

-(2/3)x+y=-4

The coefficient of y, also known as A, is negative.  To render it positive, we will multiply both sides by -1...

(2/3)x-y=4

It is now in standard form.

 

It passes through the point (-2,-5).  If we plug-into the slope-intercept equation...

-5=(2/3)(-2)-4

-5=(-4/3)-4

-5=(-4/3)-(12/3)

-5=-16/3

-5=-5 1/3

This point is NOT on the line.