find the equation of the line that passes through the following pairs of points (2,5) and (0,-2)
the slope is (-2-5)/(0-2) = 7/2
so the point-slope equation is
y-5 = 7/2 (x-2)
To find the equation of the line that passes through two points, you can use the point-slope form of a linear equation.
The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.
First, let's find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (2, 5) and (0, -2):
m = (-2 - 5) / (0 - 2)
m = -7 / -2
m = 7/2
Now that we have the slope, we can choose one of the points to use in the point-slope form. Let's use the point (2, 5).
Plugging the values into the point-slope form:
y - 5 = (7/2)(x - 2)
To simplify, distribute (7/2) to (x - 2):
y - 5 = (7/2)x - 7
Rearranging the equation to the slope-intercept form (y = mx + b):
y = (7/2)x - 7 + 5
y = (7/2)x - 2
Therefore, the equation of the line that passes through the points (2, 5) and (0, -2) is y = (7/2)x - 2.