Question

How do you best graph an equation in standard form? (Ax + By = C)

Answer 1

To graph an equation in standard form (Ax + By = C), find the x and y intercepts, plot them on a coordinate graph, and draw a straight line through these points to represent the linear equation.

Step-by-step explanation:

To graph an equation in standard form (Ax + By = C), you can start by finding the x and y intercepts, which is where the line crosses the x-axis and y-axis. To find the x-intercept, set y to 0 and solve for x. Similarly, to find the y-intercept, set x to 0 and solve for y. After you've found the intercepts, plot them on a coordinate graph.

For example, if the equation is 2x + 3y = 6, setting y to 0 gives the x-intercept as x = 3 (2*3 + 3*0 = 6). Setting x to 0 gives the y-intercept as y = 2 (2*0 + 3*2 = 6). Mark these points on the graph. A straight line should then be drawn connecting these two points, which is the graph of the equation. By doing this, you will get the visual representation of the relationship expressed as a linear equation, similar to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Answer 2

Answer: Find the x-intercept and y-intercept of the graph and graph a line between them.

Step-by-step explanation: The x and y intercepts of a graph are where the graph meets the x and y axis respectively. To find the x intercept of a graph, we can substitute in 0 for the y value, and solve for x. Here's an example:

3x + 6y = 9

Substitute 0 for y

3x + 6(0) = 9

Simplify by multiplying 6 and 0

3x = 9

Divide both sides by 3

x = 3

To find the y-intercept, do the same but substitute x for 0 instead:

3x + 6y = 9

Substitute x for 0

3(0) + 6y = 9

Simplify by multiplying 3 and 0

6y = 9

Divide both sides by 6

y =
`(9)/(6)`

Simplify by reducing the fraction

y =
`(3)/(2)` = 1.5

Now we can graph the two points we got. The first point is the x-intercept. We know y=0 because this is where the line intercepts the x-axis, and that the x value is 3 because we solved for it. We can then graph the point (3, 0). We can do the same for the y-intercept. We know x = 0 because this is where the line intercepts the y-axis, and y = 1.5 if since we solved for it. We can then graph (0, 1.5). We can now graph a line betwen these two points.