Graphing Linear equations.
How do I graph y=-4x+3
find two points on that straight line and draw a line through them with a straight edge.
easy ones are where x = 0
then
y = 3 so (0 , 3)
then where y = 0
4x=3 so x = 3/4 so (0.75 , 0)
To graph the linear equation y = -4x + 3, you can follow these steps:
Step 1: Identify the x and y intercepts
The x-intercept is the point where the graph intersects the x-axis. To find it, set y = 0 and solve for x:
0 = -4x + 3
4x = 3
x = 3/4
So, the x-intercept is (3/4, 0).
The y-intercept is the point where the graph intersects the y-axis. To find it, set x = 0 and solve for y:
y = -4(0) + 3
y = 3
So, the y-intercept is (0, 3).
Step 2: Plot the intercepts
On a graph paper, plot the x-intercept (3/4, 0) and y-intercept (0, 3) as points.
Step 3: Determine additional points
To graph the line, choose additional values for x, substitute them into the equation, and solve for y. Some commonly chosen x-values are -1, 1, and 2:
For x = -1:
y = -4(-1) + 3
y = 4 + 3
y = 7
So, (-1, 7) is a point on the line.
For x = 1:
y = -4(1) + 3
y = -4 + 3
y = -1
So, (1, -1) is another point on the line.
For x = 2:
y = -4(2) + 3
y = -8 + 3
y = -5
So, (2, -5) is another point on the line.
Step 4: Connect the points
Once you have plotted the intercepts and additional points, connect them with a straight line. This line represents the graph of the equation y = -4x + 3.
Step 5: Label the graph
Label the x-axis as "x" and the y-axis as "y". You can also add a title to your graph, such as "Graph of y = -4x + 3".
That's it! You have successfully graphed the equation y = -4x + 3.
To graph the linear equation y = -4x + 3, you can follow these steps:
Step 1: Start by creating a coordinate plane with x and y axes.
Step 2: Identify the y-intercept. In this case, the y-intercept is the point (0, 3) since the equation is in the form y = mx + b, where b is the y-intercept.
Step 3: Plot the y-intercept point (0, 3) on the graph by moving up 3 units from the origin (0, 0) on the y-axis.
Step 4: Use the slope to find additional points. The coefficient of x in the equation (-4) represents the slope of the line. The slope is the ratio of the vertical change (rise) to the horizontal change (run) that represents how the line "slopes" on the graph.
- Starting from the y-intercept point (0, 3), move down 4 units (since -4 is the slope) and move one unit to the right to find the next point. This gives you the point (1, -1).
- Repeat this process as needed to find more points. You can move up 4 units and one unit to the left from the y-intercept to find the point (-1, 7).
Step 5: Connect the plotted points. Once you have a few points on the graph, use a straightedge or ruler to connect them. This line represents the graph of the equation y = -4x + 3.
So, the graph of the equation y = -4x + 3 would be a straight line that passes through the points (0, 3), (1, -1), (-1, 7), and any other points that you find following the steps above.