Write the equation of the line that passes through the points left bracket, minus, 3, comma, minus, 4, right bracket(−3,−4) and left bracket, 7, comma, minus, 2, right bracket(7,−2). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line passing through the points (-3,-4) and (7,-2), we need to first determine the slope of the line.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points:
m = (-2 - (-4)) / (7 - (-3))
m = (-2 + 4) / (7 + 3)
m = 2 / 10
m = 1/5
Now that we have the slope of the line, we can use the point-slope form of the equation of a line. Given a point (x1, y1) and slope (m), the equation of the line is given by:
y - y1 = m(x - x1)
Choosing one of the points, (-3,-4), as (x1,y1):
y - (-4) = (1/5)(x - (-3))
y + 4 = (1/5)(x + 3)
This is the equation of the line passing through the given points in point-slope form. However, we can simplify it further by distributing the (1/5) into the parentheses:
y + 4 = (1/5)x + 3/5
Hence, the equation of the line passing through the points (-3,-4) and (7,-2) is y + 4 = (1/5)x + 3/5.