A line passes through the points (
–
14,
–
10) and (7,
–
4). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
First, we find the slope:
m = (y2 - y1) / (x2 - x1)
m = (-4 - (-10)) / (7 - (-14))
m = (-4 + 10) / (7 + 14)
m = 6 / 21
m = 2 / 7
Next, we use the point-slope form of the equation of a line to find the equation:
y - y1 = m(x - x1)
y - (-10) = 2/7(x - (-14))
y + 10 = 2/7(x + 14)
y + 10 = 2/7x + 28/7
y = 2/7x + 28/7 - 70/7
y = 2/7x - 42/7
y = 2/7x - 6
Therefore, the equation of the line passing through the points (-14, -10) and (7, -4) in slope-intercept form is y = 2/7x - 6.