The answer is: " y = - 6 " .
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Step-by-step explanation:
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To start, We find the equation of the given line ; (in "blue" ; within the "image attached");
in the slope-intercept form:
" y = mx + b " ;
in which:
"m = the slope = 0 " ; since there is no "slope";
"b" = the "y-intercept" ; or more precise, the value of the "y-coordinate" of the [point of the "y-intercept" — that is; the point at which the graph crosses the "y-axis" .].
Note: From the graph shown (Refer to image attached); the "y-intercept" is: " (0, 4) " ;
As such: " b = 4 " .
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So, the equation; in "slope intercept format" ; that is: " y = mx + b " for the original line; is: "y = 0x + 4 " .
Let us simplify this equation:
" y = 0x + 4 " ; Note: " 0x = 0 " ;
{since: "0" ; multiplied by "any value" ; results in: "0" .}.
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We are are left with " y = 4 " ;
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Now, we are asked to find the equation of the line that is "parallel" to this line and that passes through the point: " (-4, 6) ".
If such a line is "parallel" to the original line, the slope would be the same, which is "0" .
So, " y = 0x + b" ;
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Also, note the formula:
y - y₁ = m(x - x₁) ;
in which we consider the point: " (- 4, - 6) " ;
in which: " y₁ = -6 " ; and: " x₁ = -4 " ;
→ y - (-6) = m (x - (-4)) ;
→ y + 6 = m (x + 4) ;
Note: " m = 0" ;
So; " m(x + 4) " = (0)* (x + 4) = "0" ;
{since: "0" ; multiplied by "any value" ; results in: "0" .}.
→ We have:
y + 6 = 0 ;
→ Let us subtract "6" from each side of the equation;
to isolate "y" on one side of the equation;
& to write the equation for the 'perpendicular line' ; as follows:
→ y + 6 - 6 = 0 - 6 ;
to get:
→ y = - 6 ;
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The answer is: " y = - 6 " .
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Hope this helps!
Wishing you the best in your academic endeavors
— and within the "Brainly" community!
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