Graph the line with the given point and slope.

The line through​ (0,0) with slope (3/2)

1 answer

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.