Final answer:
The equation of the line passing through the points (3,6) and (7, -2) is found by first calculating the slope (m = -2) and then using the point-slope form to reach the slope-intercept form, which gives the final equation y = -2x + 12.
Step-by-step explanation:
To write an equation that contains the points (3,6) and (7, -2), you first need to calculate the slope (m) of the line that passes through these points. The formula for the slope is:
m = (Y2 - Y1) / (X2 - X1)
Plugging in our points, we get:
m = (-2 - 6) / (7 - 3) = -8 / 4 = -2
Now that we have the slope, we use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1).
Using the point (3,6), the equation becomes:
y - 6 = -2(x - 3)
Finally, to write this in slope-intercept form, we distribute and simplify:
y - 6 = -2x + 6
y = -2x + 12
The equation of the line that passes through the points (3,6) and (7, -2) is y = -2x + 12.