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?

Answer 1

To write the equation of a line in slope-intercept form (y = mx + b), we need to use the slope (m) and the y-intercept (b). We already know that the slope (m) is -1 and the line passes through the point (-5, 3).

1. Start with the slope-intercept form: \[ y = mx + b \]

2. Substitute the slope into the equation: \[ y = -1x + b \]

3. Now, we need to find the y-intercept (b). We can do this by substituting the coordinates of the point (-5, 3) into the equation: \[ 3 = -1(-5) + b \]

4. Simplify the equation: \[ 3 = 5 + b \]

5. Now, solve for b: \[ b = 3 - 5 \] \[ b = -2 \]

6. Now we can rewrite the equation using the slope and the y-intercept: \[ y = -1x - 2 \]

So, the equation of the line in slope-intercept form is: \[ y = -x - 2 \]