graph the line passing through the given point the given slope (0,1), m=-3
To graph the line passing through the point (0,1) with a slope of -3, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, m = -3, so the equation of the line is y = -3x + b.
To find the value of b, we can substitute the coordinates of the given point (0,1) into the equation and solve for b.
1 = -3(0) + b
1 = 0 + b
b = 1
So the equation of the line is y = -3x + 1.
Now we can plot the point (0,1) on the graph and use the slope to find a second point. The slope of -3 means that for every 1 unit we move to the right on the x-axis, we move down 3 units on the y-axis.
Starting from the point (0,1), we can move 1 unit to the right and 3 units down to get the point (1, -2).
Plot these two points on the graph and draw a straight line passing through them:
- Plot (0,1) as a point on the graph.
- Plot (1, -2) as a point on the graph.
- Draw a straight line passing through these two points.
The graph of the line passing through the point (0,1) with a slope of -3 is a downward-sloping line that goes through the points (0,1) and (1, -2).