Question

Draw a graph of the line that contains the given point and has the given slope.
(-5,0) and m=1/8

Answer 1

To graph a line with a given point and slope, we can use the point-slope form of a linear equation. The point-slope form of a line's equation is:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is the given point and \(m\) is the slope.

In this case, the point is \((-5, 0)\) and the slope is \(m = \frac{1}{8}\). Plugging these values into the point-slope formula, we get:

\[
y - 0 = \frac{1}{8}(x - (-5))
\]
\[
y = \frac{1}{8}(x + 5)
\]

Next, let’s simplify this equation:

\[
y = \frac{1}{8}x + \frac{5}{8}
\]

Now, we can find a couple of points to help plot this line.

1. Start with the given point \((-5, 0)\).
2. You can find another point by choosing a value for \(x\). Let's choose \(x = -1\):

\[
y = \frac{1}{8}(-1) + \frac{5}{8} = -\frac{1}{8} + \frac{5}{8} = \frac{4}{8} = \frac{1}{2}
\]

So, another point on the line is \((-1, \frac{1}{2})\).

3. Now choose another \(x\) value, say \(x = 3\):

\[
y = \frac{1}{8}(3) + \frac{5}{8} = \frac{3}{8} + \frac{5}{8} = \frac{8}{8} = 1
\]

This gives us another point: \((3, 1)\).

Now we have three points:
1. \((-5, 0)\)
2. \((-1, \frac{1}{2})\)
3. \((3, 1)\)

To graph this line, you can:

1. Plot the points on a coordinate plane.
2. Draw a line through these points, extending it in both directions.

The slope of \(\frac{1}{8}\) means that for every 8 units you move to the right on the x-axis, you move up 1 unit on the y-axis. This will help you visualize the slope as you draw the line.

Unfortunately, I am unable to create visual graphics, but this method will guide you in accurately plotting the line on graph paper or using graphing software.