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)%0D%0AResponses%0D%0A%0D%0Ay=−x+3%0D%0Ay equals negative x plus 3%0D%0A%0D%0Ay=−x−2%0D%0Ay equals negative x minus 2%0D%0A%0D%0Ay=x−1%0D%0Ay equals x minus 1%0D%0A%0D%0Ay=−x−5

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we start with the slope and the point given.

1. The slope (m) is -1.
2. The line passes through the point (-5, 3). This means that when x = -5, y = 3.

We can use the point-slope form of the equation of a line first:

\[ y - y_1 = m(x - x_1) \]

where (x_1, y_1) is the point on the line. Plugging in our values:

\[ y - 3 = -1(x - (-5)) \] \[ y - 3 = -1(x + 5) \] \[ y - 3 = -x - 5 \]

Next, we simplify it:

\[ y = -x - 5 + 3 \] \[ y = -x - 2 \]

So, the equation in slope-intercept form is:

y = -x - 2

The correct response from the options provided is: y = -x - 2 (or "y equals negative x minus 2").