A line passes through the points (-5, 9) and (15,17). Write its equation in slope-intercept form
The slope of the line passing through the two points can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-5, 9) and (x2, y2) = (15, 17).
m = (17 - 9) / (15 - (-5))
= 8 / (15 + 5)
= 8 / 20
= 2/5
Now that we have the slope, we can substitute it into the equation:
y - y1 = m(x - x1)
Using (x1, y1) = (-5, 9):
y - 9 = (2/5)(x - (-5))
y - 9 = (2/5)(x + 5)
Expanding the equation:
y - 9 = (2/5)x + (2/5)(5)
y - 9 = (2/5)x + 2
Rearranging the equation to slope-intercept form:
y = (2/5)x + 2 + 9
y = (2/5)x + 11
Therefore, the equation of the line in slope-intercept form is y = (2/5)x + 11.