Final answer:
To find the equation of the line passing through points (-0, 6) and (3, 2), calculate the slope, then use the point-slope form, and finally convert it to slope-intercept form, resulting in the equation y = (-4/3)x + 6.
Step-by-step explanation:
To write the equation of the line that passes through the points (-0, 6) and (3, 2), we must first find the slope (m) of the line. This can be done using the formula for the slope of a line passing through two points (x1, y1) and (x2, y2):
m = (y2 - y1) / (x2 - x1)
In this case, substituting the given points:
m = (2 - 6) / (3 - (-0))
m = (-4) / (3)
m = -4/3
Now that we have the slope, we can use the point-slope form of the equation of a line: y - y1 = m(x - x1). Let's use the point (-0, 6):
y - 6 = (-4/3)(x - 0)
To write this equation in slope-intercept form, y = mx + b, we distribute the slope (-4/3) and then add 6 to both sides:
y = (-4/3)x + 6
Therefore, the equation of the line that passes through the points (-0, 6) and (3, 2) is y = (-4/3)x + 6.