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 (3,3)
To find the equation of the line that passes through the points (-3, 5) and (3, 3), we can use the point-slope form:
y - y1 = m(x - x1)
where (x1, y1) are coordinates of one point and m is the slope of the line.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the given points, we have:
m = (3 - 5) / (3 - (-3))
m = -2 / 6
m = -1/3
Now, let's choose one of the points, (-3, 5), to substitute into the point-slope form:
y - 5 = (-1/3)(x - (-3))
y - 5 = (-1/3)(x + 3)
To convert it into the slope-intercept form (y = mx + b), let's simplify the equation:
y - 5 = (-1/3)(x + 3)
y - 5 = (-1/3)x - 1
y = (-1/3)x - 1 + 5
y = (-1/3)x + 4
Therefore, the equation of the line in point-slope form is y - 5 = (-1/3)(x + 3), and the equation in slope-intercept form is y = (-1/3)x + 4.