Question 825796
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(completed solution here.)

Hi, there--

THE PROBLEM:

The line containing A(0,7) and B(7,0)
Find:
M= ?
Point slope form= ?
Slope intercept form= ?
Standard form= ? 

A SOLUTION:

Find the slope M of the find between these two points.

{{{M=(y[B]-y[A])/(x[B]-x[A])}}}
{{{M=(0-7)/(7-0)}}}
{{{M=-1}}}

The slope of this line is -1.

Find the equation for the line in point-slope form. For point-slope form we need the slope and one point. I'll use point A but either one will work. Point-slope form is
{{{y-y[A])=M*(x-x[A])}}}

Substitute values for the coordinates for point A and the slope.
{{{y-(7)=(-1)*(x-(0))}}}

This is the equation in point-slope form.
{{{y-7=-(x-0)}}}

Rewrite this equation in slope-intercept form. Slope-intercept form looks like y=mx+b.

{{{y-7=-(x-0)}}}

Simplify the right side.
{{{y-7=-x}}}

Isolate y on the left. Simplify. This is the equation in slope-intercept form.
{{{y=-x+7}}}

Rewrite the equation in standard form. Standard form looks like Ax + By = C, where A, B, and C are constants.

{{{y=-x+7}}}

Add x to both sides.
{{{x+y=7}}}


Hope this helps! Feel free to email if you have any questions.

Mrs. Figgy
math.in.the.vortex@gmail.com
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