## Write an equation for the line passing through the given point and having the given slope. (10,6), m= 1 The equation of t

Question

Write an equation for the line passing through the given point and having the given slope.
(10,6), m= 1
The equation of the line is:
(Type your answer in slope-iritercept form. Use integers or fractions for any numbers in the equation.)

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7 days 2021-09-13T10:48:56+00:00 1 Answer 0

1. Answer:  The equation, in “slope-intercept form” ; is:

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→   ” y  =   x  +  4  ” .

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Step-by-step explanation:

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Use the formula for linear equations;  written in “point-slope format” ;

which is:

y −  y₁  = m( x −  x₁ )  ;

We are given the slope, “m” ;  has a value of:  “1 ” ;

that is;  “ m = 2 ” .

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We are given the coordinates to 1 (one) point on the line; in which the coordinates are in the form of :

” ( x₁ , y₁ ) ” ;

→   that given point is:  “(10, 6)” ;

in which:  x₁ =  10 ;

y₁  =  6 .

→ Given:  The slope, “m” equals “1” ;  ________________________________________________

Let’s plug our known values into the formula:

→  ”  y  −  y₁  = m( x − x₁ ) ”  ;

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→   As follows:

→   ” y  −  10  = 1(x − 6) ;

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Now, focus on the “right-hand side of the equation” ;

→    1(x  −  6) = ? ;   Simplify.

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Note the “distributive property” of multiplication:

→  a(b + c) =  ab   +   ac ;

As such:  ” 1(x  −  6) =  (1*x)  +  (1 * -6) ” ;

=  1x   + (-6) ;

=   x  −  6 ;

[Note that:  ” 1 x = 1 * x = x ” ;

[Note that   ” + (-6) ”  =  ” ( ” − 6 ” ) .] ;

→  {since:  “Adding a negative” is the same as:

“subtracting a positive.”} ;

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Now, let us bring down the “left-hand side of the equation” ; &

rewrite the entire equation; as follows:

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→   ”  y  −  10  =   x  −  6 ” ;

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Note:  We want to rewrite the equation in “slope-intercept form” ;

that is;  “ y = mx + b ”  ;

in which:  “y” ; stands alone as a single variable on the “left-hand side” of the equation;  with “no coefficients” [except for the “implied coefficient” of ” 1 “} ;

“m” is the coefficient of “x” ;

and the “slope of the line” ;

Note that “m” may be a “fraction or decimal” ; and may be “positive or negative.

If the slope is “1” ; (that is “1 over 1″ ; or: “” ;

then,  “ m = 1 ” ;  and we can write ” 1x ” as simply “x” ; since the implied coefficient is1” ;

→  since ” 1” , multiplied by any value {in our case, any value for “x”} , equals that same value.

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“b”  refers to the “y-intercept” of the graph of the equation;

that is; the “y-value” of the point at which the graphed line of the equation crosses the “y-axis” ;

that is, the “y-value” of the coordinates of the point at which the graphed line of the equation crosses the “y-axis” ;

that is, the [“y-value” of the]  y-intercept” .

Note that the value of “b” may be positive or negative, and may be a decimal or fraction.

If the value for “b” is negative, the equation can be written in the form:

” y = mx – b ” ;

{since:  ” y = mx + (-b) ”  is a bit tedious .}

If the y-intercept is “0” ; (i.e. the line crosses the y-axis at the origin, at point:  ” (0,0) ” ;

then we simply write the equation as:  “y = mx ” ;

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So;  we have:              →   ” y   10  =  x  −  6 ” ;

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→   We want to rewrite our equation in slope-intercept form,

that is;  ” y = mx + b ” ;  as explained above.

We can add “10” to each side of the equation ; to isolation the “y” on the “left-hand side” of the equation:

→  ” y  −  10  + 10  =  x  − 6  +  10 ” ;

to get:

→  ” y  =  x  +  4 ” ;

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Note:  This answer:  ” y = x + 4 ” ;

→  is written in the “slope-intercept format”;

→   “ y = mx +  b ”  ;

in which:  “y” is isolated as a single variable on the “left-hand side of the equation” ;

The slope of the equation is “1” ; or an implied value of “1” ;

that is;   ” m  = 1 ” ;

“b  =  4 ” ;

→  {that is;  the “y-value” of the  “y-intercept” —  “(0, 4)” — of the graph of the equation is:  “4 “.} .

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