Complete the point-slope equation of the line through ( 6 , 4 ) (6,4)left parenthesis, 6, comma, 4, right parenthesis and ( 7 , 2 ) (7,2)left parenthesis, 7, comma, 2, right parenthesis. use exact numbers. y − 2 = y−2=y, minus, 2, equals

The point-slope equation of the line through (6,4), and (7,2) is given as:

The point-slope equation of that straight line.

The point slope form of a straight line typically looks like:

Slope ( represented by m, say) can be calculated by the evaluating the ratio of how much growth happened in how much difference in the x axis.

Here, the point are (6,4) and (7,2)

They represent:

as x goes from 6 to 7 (which means 1 unit growth),

the y goes from 4 to 2 (which means opposite 2 units ie -2 unit growth)

Thus, slope will be their ratio as:

The line equation having slope m is represented as y = mx + c.

Putting coordinate values (6,4) to evaluate the value of intercept c:

Thus, the equation of the considered line is: y = -2x + 16.

Converting it in the point slope intercept form, with

Thus, the point-slope equation of the given line is:

Learn more about equation of straight line here:

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y-4 = -2(x-6)

Step-by-step explanation:

I'd suggest you use a symbolic presentation only to describe your two points:  (6,4) and (7,2).  You want to determine the point-slope equation of the line thru these two points.  As you go from (6,4) to (7,2), x increases by 1 and y decreases by 2; thus, the slope of this line is m = rise / run = -2/1 = -2.

Borrowing the info from one of the given points, we're now ready to write out the point-slope equation of this line:

y-4 = -2(x-6).  Note that y-2 = -2(x-7) is equivalent.

may i see the picture? it would a lot, xox