Question

Graph the line with the given point and slope.
The line through ​(1​,negative 3​) with slope two thirds

Answer 1

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

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point and m is the slope.

In this case, the given point is (1, -3) and the slope is 2/3. Plugging these values into the point-slope form, we have:

y - (-3) = (2/3)(x - 1)

Simplifying this equation gives:

y + 3 = (2/3)(x - 1)

To graph the line, we can plot the given point (1, -3) and use the slope to find additional points. Since the slope is 2/3, we can move 2 units up and 3 units to the right from the point (1, -3) to find another point on the line. This gives us the point (4, -1).

Now, we can connect the two points (1, -3) and (4, -1) to graph the line.

The graph of the line is shown below:

graph{(1, -3)(4, -1)}