To graph the line through the point (0,0) with a slope of 3/2, we can use the slope-intercept form of a linear equation, which is y = mx + b.
Given that the slope (m) is 3/2, we have y = (3/2)x + b.
Since the line passes through the point (0,0), we can substitute x = 0 and y = 0 into the equation to find the value of b:
0 = (3/2)(0) + b
0 = 0 + b
b = 0
Now we have y = (3/2)x + 0, which simplifies to y = (3/2)x.
To graph the line, we can plot several points that satisfy the equation. Let's choose x = -2, -1, 0, 1, and 2:
When x = -2:
y = (3/2)(-2)
y = -3
So the point (-2, -3) is on the line.
When x = -1:
y = (3/2)(-1)
y = -3/2
So the point (-1, -3/2) is on the line.
When x = 0:
y = (3/2)(0)
y = 0
So the point (0, 0) is on the line.
When x = 1:
y = (3/2)(1)
y = 3/2
So the point (1, 3/2) is on the line.
When x = 2:
y = (3/2)(2)
y = 3
So the point (2, 3) is on the line.
Now we can plot these points on a coordinate plane and draw a straight line passing through them:
|
|
| • (2,3)
| • (1,3/2)
| /
| /
| /
• (0,0)
_____________________
-2 -1 0 1 2
The graph of the line passing through the point (0,0) with a slope of 3/2 is a diagonal line that extends from the bottom left of the graph to the top right.
Graph the line with the given point and slope.
The line through (0,0) with slope (3/2)
1 answer