Answer:
The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
Explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We have the point (-6,8) and a slope of -5/3.
Step 1: Use the point-slope formula to find the equation of the line in point-slope form.
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point.
y - 8 = (-5/3)(x - (-6))
Simplify this equation:
y - 8 = (-5/3)(x + 6)
Step 2: Convert the equation to slope-intercept form.
Distribute (-5/3) to get:
y - 8 = (-5/3)x - 10
Add 8 to both sides:
y = (-5/3)x - 2
This is the equation of the line in slope-intercept form. Therefore, the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.