Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form.
(-3,5) and (9,1)
To find the equation of a line given two points, we can use the point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points and m is the slope.
First, let's calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= (1 - 5) / (9 - (-3))
= -4 / 12
= -1/3
Using the point-slope form with one of the given points (-3, 5), we have:
y - 5 = -1/3(x - (-3))
Simplifying the equation:
y - 5 = -1/3(x + 3)
y - 5 = -1/3x - 1
y = -1/3x + 4
Therefore, the equation in point-slope form is y - 5 = -1/3(x + 3) and in slope-intercept form is y = -1/3x + 4.