Graph the line with slope g passing through the point (2, - 5).

Question

Graph the line with slope g passing through the point (2, - 5).

Answer 1

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. However, we don't know the y-intercept in this case, so we'll use the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

We know the slope is g, so plugging in (2, -5) gives:

y - (-5) = g(x - 2)

Simplifying, we get:

y + 5 = g(x - 2)

Now let's rearrange this equation into slope-intercept form by solving for y:

y = g(x - 2) - 5

So our equation is y = gx - 2g - 5. This line passes through the point (2, -5) and has a slope of g. To graph it, we can plot the point (2, -5) and then use the slope to find additional points on the line. For example, if g = 2, we can start at (2, -5) and use the slope to find the point (3, -3) and (4, -1). If g = -1/2, we can start at (2, -5) and use the slope to find the point (1, -6) and (3, -4).

Here's an example graph with g = 2:

![Line with slope 2 passing through point (2, -5)](https://i.imgur.com/dZqL0J4.png)

Answer 2

To graph the line with slope g passing through the point (2, -5), follow these steps:

Step 1: Plot the given point (2, -5) on a Cartesian plane. This point represents one point on the line.

Step 2: Use the slope g to determine a second point on the line. The slope of a line represents the change in the y-coordinates divided by the change in the x-coordinates. In other words, it tells you how much the line rises or falls vertically for every unit it moves horizontally.

Step 3: Let's assume the slope g is 3/2. Starting from the point (2, -5), you can use the slope to find another point on the line. Since the slope is 3/2, you can interpret this as "for every 2 units the line moves horizontally, it moves up 3 units vertically."

Starting from the point (2, -5), you can move 2 units to the right and 3 units up to reach another point on the line. This gives you the point (4, -2).

Step 4: Once you have the two points (2, -5) and (4, -2), draw a straight line passing through these two points. This line represents the graph of the line with slope g passing through the point (2, -5).

Note: If you have the actual value of the slope g, you can replace the slope g with that value in step 3 to find the second point on the line.