The equation of the line is y = (1/3)x - (2/3), and the difference c - m is -1.
To find the equation of the line given its x-intercept and y-intercept, we can use the fact that the x-intercept occurs when y = 0 and the y-intercept occurs when x = 0.
Let's denote the x-intercept as (2, 0) and the y-intercept as (0, -2/3).
X-Intercept (2, 0):
When x = 2, y = 0. Plug these values into the equation y = mx + c:
0 = 2m + c
Y-Intercept (0, -2/3):
When y = -2/3, x = 0. Plug these values into the equation y = mx + c:
-2/3 = c
Now, let's solve for m and c:
From the x-intercept: c = -2m
From the y-intercept: c = -2/3
Since both expressions equal c, we can set them equal to each other:
-2m = -2/3
Solving for m:
m = 1/3
Now, we can find c:
c = -2 * (1/3) = -2/3
Finally, to find c - m:
-2/3 - 1/3 = -3/3 = -1
Complete question:
The function that has an x-intersecpt of 2 and a y-intercept of -2/3. Then the equation of line is y = mx + c. Find c − m.