Question 13(Multiple Choice Worth 1 points) (04.02 MC) The equation of line $$ A B $$ is $$ y=5 x+1 $$. Write an equation of a line parallel to line $$ A B $$ in slope-intercept form that contains point $$ (4,5) $$. $$ y=5 x-15 $$ $$ y=5 x+15 $$ $$ y=\frac{1}{5} x+\frac{21}{5} $$ $$ y=\frac{1}{5} x-\frac{29}{5} $$

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\textbf{Step 1:}
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Since line $$ AB $$ is given by $$ y = 5x + 1 $$, its slope is $$ 5 $$. Any line parallel to it must also have a slope of $$ 5 $$.

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\textbf{Step 2:}
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The equation of a line in slope-intercept form is 
$$
y = mx + b,
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where $$ m $$ is the slope and $$ b $$ is the $$ y $$-intercept. Since the slope must be $$ 5 $$, the equation takes the form:
$$
y = 5x + b.
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\textbf{Step 3:}
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We know the line passes through the point $$ (4,5) $$. Substitute $$ x = 4 $$ and $$ y = 5 $$ into the equation:
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5 = 5(4) + b.
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$$
5 = 20 + b.
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\textbf{Step 4:}
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Solve for $$ b $$:
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b = 5 - 20 = -15.
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\textbf{Step 5:}
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Substitute $$ b = -15 $$ back into the equation of the line:
$$
y = 5x - 15.
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\textbf{Final Answer:}
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$$ y = 5x - 15 $$.
The equation of the line parallel to $$ y = 5x + 1 $$ that passes through the point $$ (4,5) $$ is $$ y = 5x - 15 $$.

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