Final answer:
To find the equation of a line passing through two points, we first find the slope and then use one of the points in the slope-intercept form. The equation of the line passing through (-3,-8) and (5,6) is y + 8 = (7/4)(x + 3).
Step-by-step explanation:
To find the equation of a line that passes through two points, we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one point and m is the slope of the line. First, we need to find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates (-3,-8) and (5,6), we find that the slope is m = (6 - (-8)) / (5 - (-3)) = 14 / 8 = 7/4. Now, we can choose one point and plug it along with the slope into the first formula to find the equation. Let's use the point (-3,-8):
y - (-8) = (7/4)(x - (-3))
Simplifying, we get y + 8 = (7/4)(x + 3) as the equation of the line.
Learn more about Equations of Lines