Write the equation of the line that passes through the points left bracket, minus, 9, comma, minus, 9, right bracket(−9,−9) and left bracket, minus, 8, comma, 1, right bracket(−8,1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line that passes through the points (-9,-9) and (-8,1), we can use the point-slope form of the equation.
The point-slope form of a linear equation is given by: y - y1 = m(x - x1), where (x1, y1) is the coordinates of a point on the line, and m is the slope of the line.
First, let's find the slope (m) using the formula: slope (m) = (change in y) / (change in x).
change in y = 1 - (-9) = 10
change in x = -8 - (-9) = 1
Therefore, the slope (m) = change in y / change in x = 10 / 1 = 10.
Now, we can choose either of the given points to substitute into the point-slope form. Let's use the point (-9,-9):
y - (-9) = 10(x - (-9))
y + 9 = 10(x + 9)
To simplify further, we can distribute the 10:
y + 9 = 10x + 90
Now, to get the equation into point-slope form, we can subtract 9 from both sides:
y = 10x + 90 - 9
Finally, we can simplify further:
y = 10x + 81
Therefore, the equation of the line that passes through the points (-9,-9) and (-8,1) in point-slope form is: y = 10x + 81.