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: