Answer:
y - 4 = 1/3(x + 5)
Explanation:
The general equation for the point-slope form of a line is given by:
y - y1 = m(x - x1), where
- (x1, y1) is a point on the line,
- and m is the slope of the line.
Step 1: To find the equation of the line through (-5, 4) and (1, 6), we first need to find the slope of the line using the slope formula, which is:
m = (y2 - y1) / (x2 - x1), where
- (x1, y1) are one point on the line,
- and (x2, y2) are another point on the line
We can allow (-5, 4) to be our (x1, y1) point and (1, 6) to be our (x2, y2) point:
m = (6 - 4) / (1 - (-5))
m = 2 / (1 + 5)
m = 2/6
m = 1/3
Now we can use the point-slope form of the equation with either of the two points.
- Since we already used (-5, 4) as our (x1, y1) point, let's use it for the point-slope form:
y - 4 = 1/3(x - (-5))
y - 4 = 1/3(x + 5)
Thus, the point-slope equation of the line through (-5, 4) and (1, 6) is:
y - 4 = 1/3(x + 5)