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: "[tex]\frac1}{1}[/tex]" ;
then, " m = 1 " ; and we can write " 1x " as simply "x" ; since the implied coefficient is "1" ;
→ 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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→ which is our answer.
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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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Hope this answer is helpful!
Best wishes to you in your academic pursuits
— and within the "Brainly" community!
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