Draw a line with a slope of one-fourththrough the point (0, –4).
A. graphThe graph follows a line down and to the right. The line passes through the point left parenthesis negative 4 comma negative 4 right parenthesis to the point left parenthesis 0 comma negative 6 right parenthesis.
B. graph
C. graph
D. graph
B. graph
To draw a line with a slope of one-fourth through the point (0, –4), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Substituting m = 1/4 and (x1, y1) = (0, –4), we get:
y - (-4) = 1/4(x - 0)
Simplifying this equation, we get:
y + 4 = 1/4x
y = 1/4x - 4
To graph this line, we can use the slope-intercept form of the equation:
y = mx + b
where m is the slope and b is the y-intercept.
Comparing the equations, we see that the slope is the same (m = 1/4) but the y-intercept is different (b = –4). So the graph of the line will be parallel to the line y = 1/4x, but shifted downward by 4 units.
To plot the line, we can start at the y-intercept (0, –4) and use the slope to find another point. Since the slope is rise over run, we can go up 1 unit and right 4 units from the y-intercept to get the point (4, –3). Then we can draw a straight line through these two points to get the graph:
```
| *
-6 + \
| \
-5 + \
| *
-4 + \
| \
-3 + *
| \
-2 + \
| \
-1 + *
| \
|__|__|__|__|__|__|__|__|__|__
0 1 2 3 4 5 6 7