Simpson Powell
05/14/2024 · Senior High School
1 point Find the equation of the line that is parallel to \( y=2 x+5 \) and passes through the point \( (4,3) \), Write your answer in slope-interceptf Answer: \( y= \) type your answer...
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To find the equation of a line that is parallel to \( y = 2x + 5 \) and passes through the point \( (4, 3) \), we first note that parallel lines have the same slope. The slope of the given line \( y = 2x + 5 \) is \( 2 \).
Now, we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through. Here, \( m = 2 \), \( x_1 = 4 \), and \( y_1 = 3 \).
Substituting these values into the point-slope form:
\[
y - 3 = 2(x - 4)
\]
Now, we simplify this equation:
\[
y - 3 = 2x - 8
\]
Adding \( 3 \) to both sides gives:
\[
y = 2x - 5
\]
Thus, the equation of the line that is parallel to \( y = 2x + 5 \) and passes through the point \( (4, 3) \) is:
\[
\boxed{y = 2x - 5}
\]
Quick Answer
The equation of the line is \( y = 2x - 5 \).
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