Analyze the linear function whose slope is −3 and passes through the coordinate pair (−2,9) . Which linear function matches this line?(1 point) Responses y= −2x −3 y equals negative 2 x minus 3 y= −3x +3 y equals negative 3 x plus 3 y= 3x −3 y equals 3 x minus 3 y=−3x +9
To find the linear function that matches the given information, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) are the coordinates of a point on the line.
In this case, the given slope is -3 and the coordinate pair is (-2, 9). Substituting these values into the point-slope form equation, we have:
y - 9 = -3(x - (-2))
Simplifying, we get:
y - 9 = -3(x + 2)
Expanding the brackets, we have:
y - 9 = -3x - 6
Finally, rearranging the equation to the slope-intercept form (y = mx + b), we have:
y = -3x + 3 + 9
y = -3x + 12
Therefore, the linear function that matches the given line is y = -3x + 12.