Final answer:
The equation of the line that passes through the points (-6,8) and (3,-4) is y = (-4/3)x + 16.
Step-by-step explanation:
The equation of a line can be found using two points on the line by first calculating the slope of the line (represented as m in the slope-intercept form, y = mx + b) and then using the slope and one of the points to solve for the y-intercept (represented as b).
Step 1: Calculating the Slope (m)
To find the slope of the line that passes through the points (-6,8) and (3,-4), use the formula:
m = (y2 - y1) / (x2 - x1)
Thus,
m = (-4 - 8) / (3 - (-6)) = -12 / 9 = -4/3
Step 2: Calculating the Y-intercept (b)
Using the slope (-4/3) and one of the points, say (-6,8), plug into the slope-intercept formula:
y - y1 = m(x - x1)
Substituting the values gives:
8 - (-4/3)(-6) = -4/3 * x + b
Solving for b gives:
8 + 8 = -4/3 * x + b
16 = b
Step 3: The Equation of the Line
So, the equation of the line in slope-intercept form is:
y = (-4/3)x + 16