Answer:
Therefore, the equation of the line that passes through the points (0, 4) and (-6, 8) is:
y = (-2/3)x + 4
Explanation:
The equation of a line that passes through two points can be found using the slope-intercept form:
y = mx + b
Where:
m is the slope of the line
b is the y-intercept of the line
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Where:
(x1, y1) are the coordinates of the first point
(x2, y2) are the coordinates of the second point
In this case, the first point is (0, 4) and the second point is (-6, 8). Plugging these values into the formula, we get:
m = (8 - 4) / (-6 - 0)
Simplifying the expression, we get:
m = 4 / -6
m = -2/3
Now that we know the slope, we can find the y-intercept by substituting the coordinates of one of the points and the slope into the slope-intercept form:
y = (-2/3)x + b
We can use the coordinates of the first point, (0, 4), to solve for b. Substituting these values into the equation, we get:
4 = (-2/3)(0) + b
Simplifying the expression, we get:
4 = b