Question

find the equation of a line that is parallel to ( y = 5x + 7 ) and passes through ( (4, 3) ).
a ( y = 5x + 3 )
b ( y = 5x - 17 )
c ( y = 5x + 17 )
d ( y = \frac{1}{5}x - 17 )
e ( y = -\frac{1}{5}x + 17 )

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=5x+7$, the slope $m=5$. So the target line has $m=5$, and its form is $y=5x+b$.

Step2: Solve for y-intercept $b$

Substitute the point $(4,3)$ into $y=5x+b$:
$3 = 5(4) + b$
$3 = 20 + b$
$b = 3 - 20 = -17$

Step3: Write final equation

Substitute $b=-17$ into $y=5x+b$ to get the line equation.

Answer:

B. $y = 5x - 17$