what is the effect on the graph of the equation 6x+3y=12 if 12 is changed to 36?
let's write the old and new equations:
(i) 6x+3y=12
(ii) 6x+3y=36
notice that they have the same slope, thus the new line (ii) is parallel to the original line (i).
also , transforming this into slope-intercept form, they become
(i) y = -2x + 4
(ii) y = -2x + 12
the y-intercept of (i) is at (0,4) while (ii) is at (0,12). thus the new line moved 8 units up from the original line.
hope this helps~ :)
To understand the effect on the graph of the equation when the value of 12 is changed to 36, we need to consider the slope-intercept form of the equation.
The given equation is in standard form: 6x + 3y = 12
To convert it to slope-intercept form, we need to isolate y:
3y = 12 - 6x
y = (12 - 6x) / 3
y = 4 - 2x
In slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
From the equation y = 4 - 2x, we can see that the slope is -2 and the y-intercept is 4.
Now, let's consider what happens when the value of 12 is changed to 36.
The new equation becomes 6x + 3y = 36.
To find the new equation in slope-intercept form, we isolate y:
3y = 36 - 6x
y = (36 - 6x) / 3
y = 12 - 2x
From this updated equation, we can see that the new slope is -2 (which didn't change) and the new y-intercept is 12 (which increased from 4 to 12).
In terms of the graph, changing the value of 12 to 36 shifted the graph upward, as the y-intercept increased from 4 to 12, while the slope remained the same.