Question

Graph the line with the given point and slope.
Through ​(0​,3​); slope=-1/2

Answer 1

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

y - y1 = m(x - x1)

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

In this case, the given point is (0, 3) and the slope is -1/2. We can substitute these values into the point-slope form to get:

y - 3 = -1/2(x - 0)

Simplifying this equation, we have:

y - 3 = -1/2x

To graph this line, we can first plot the given point (0, 3) on the graph. Then, using the slope -1/2, we can find another point on the line.

From the point (0,3), we can go "down 1 and to the right 2" to find the next point.

So, starting from (0,3), we can move down 1 unit and right 2 units to get the point (2, 2).

Now, we can connect these two points with a straight line to graph the line.

The graph of the line through (0, 3) with a slope of -1/2 is a downward-sloping line that passes through the points (0, 3) and (2, 2).