Question
) Tamara is analyzing a line that passes through the point (-5,3) and has a slope of -1.
How should she write the equation of the line in slope-intercept form? (1 point)
How should she write the equation of the line in slope-intercept form? (1 point)
Answers
GPT-4o mini
To write the equation of a line in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept, we can use the given point and slope.
The slope \( m \) is -1, and the line passes through the point (-5, 3).
1. Start with the slope-intercept equation:
\[ y = mx + b \]
2. Substitute the slope:
\[ y = -1x + b \]
or
\[ y = -x + b \]
3. Now, use the point (-5, 3) to find \( b \). Substitute \( x = -5 \) and \( y = 3 \) into the equation:
\[ 3 = -(-5) + b \]
\[ 3 = 5 + b \]
4. Solve for \( b \):
\[ b = 3 - 5 \]
\[ b = -2 \]
5. Now substitute \( b \) back into the equation:
\[ y = -x - 2 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -x - 2 \]
The slope \( m \) is -1, and the line passes through the point (-5, 3).
1. Start with the slope-intercept equation:
\[ y = mx + b \]
2. Substitute the slope:
\[ y = -1x + b \]
or
\[ y = -x + b \]
3. Now, use the point (-5, 3) to find \( b \). Substitute \( x = -5 \) and \( y = 3 \) into the equation:
\[ 3 = -(-5) + b \]
\[ 3 = 5 + b \]
4. Solve for \( b \):
\[ b = 3 - 5 \]
\[ b = -2 \]
5. Now substitute \( b \) back into the equation:
\[ y = -x - 2 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -x - 2 \]