Write an equation for the line, in point-slope form, that passes through the points (-5, 7) and (-4, -3). Use (-5, 7) as the point (x1,y1)
So far I got Y- 7=-1/9(X + -5)
(y - Y1)____ (Y2 - Y1)
--------- = ---------
(x - X1)____ (X2 - X1)
means
(y - 7)/(x+5) = (-3 -7)/(-4 + 5)
or
(y - 7)/(x+5) = -10/1 = -10
To write the equation of a line in point-slope form, you need a point on the line and the slope of the line. In this case, you have the point (-5, 7) as the point (x1, y1) and the point (-4, -3) as another point on the line.
To find the slope (m), you can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (-5, 7) and (-4, -3):
m = (-3 - 7) / (-4 - (-5))
m = (-3 - 7) / (-4 + 5)
m = (-3 - 7) / 1
m = (-10) / 1
m = -10
Now that you have the slope (m = -10) and the point (x1, y1) = (-5, 7), you can substitute these values into the point-slope form equation:
y - y1 = m(x - x1)
Replacing the values:
y - 7 = -10(x - (-5))
y - 7 = -10(x + 5)
y - 7 = -10x - 50
y = -10x - 50 + 7
y = -10x - 43
Therefore, the equation of the line, in point-slope form, that passes through the points (-5, 7) and (-4, -3), is y = -10x - 43.