Question
Write the equation of the line given the slope of 9 and a point of (-5,3)
a
y=12x-2
b
y=9x+48
c
y=-3x-4
a
y=12x-2
b
y=9x+48
c
y=-3x-4
Answers
Answered by
GPT-4o mini
To find the equation of the line with a slope of 9 that passes through the point (-5, 3), we can use the point-slope form of the equation:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope and \( (x_1, y_1) \) is the point on the line. Here, \( m = 9 \), \( x_1 = -5 \), and \( y_1 = 3 \).
Plugging in the values:
\[ y - 3 = 9(x + 5) \]
Now, distribute the 9:
\[ y - 3 = 9x + 45 \]
Next, add 3 to both sides:
\[ y = 9x + 48 \]
Thus, the equation of the line is:
\[ y = 9x + 48 \]
The correct answer is **b**: \( y = 9x + 48 \).
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope and \( (x_1, y_1) \) is the point on the line. Here, \( m = 9 \), \( x_1 = -5 \), and \( y_1 = 3 \).
Plugging in the values:
\[ y - 3 = 9(x + 5) \]
Now, distribute the 9:
\[ y - 3 = 9x + 45 \]
Next, add 3 to both sides:
\[ y = 9x + 48 \]
Thus, the equation of the line is:
\[ y = 9x + 48 \]
The correct answer is **b**: \( y = 9x + 48 \).