Write the equation of the line that passes through the points (4,-3) and (8,5). 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 (4,-3) and (8,5), we need to find the slope of the line and use one of the two points.
The slope of a line passing through two points, (x1, y1) and (x2, y2), is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4,-3) and (8,5):
m = (5 - (-3)) / (8 - 4)
m = 8 / 4
m = 2
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (4,-3):
y - (-3) = 2(x - 4)
y + 3 = 2(x - 4)
y + 3 = 2x - 8
y = 2x - 8 - 3
y = 2x - 11
Therefore, the equation of the line passing through the points (4,-3) and (8,5) is y = 2x - 11.