x+3y=3
Answers:
You need to convert the equation into slope-intercept form (y= mx + b)
x + 3y = 3
(subtract x from both sides) 3y = -x + 3
(divide both sides by 3) y = (-1/3)x + 1
The slope, or gradient, is -1/3 (negative one-third), and the y-intercept is 1.
The easiest way to solve this problem is this:
solve your equation for y ==.> 3y = -x + 3 ==> y = -1/3x +1
Your y intercept is 1 (when x = 0, y = 1)
And your slope (gradient) is -1/3.
In standard form [In term's of 'y'] this equation would look like:
Y = -X/3 + 1 [remember the X is negative]
The 'Gradient' is another word for the slope. Slope is the ratio by which the line decreases or increases. The slope is usually the coefficient associated with the X variable in Linear equations. In this case, your process to find the gradient would be:
-1X/3
Eliminating the X variable and leaving only its coefficient:
-1/3
So your gradient is -1/3 [negative 1 over 3]
The y-intercept is when the line that your linear equation forms crosses the Y-axis in an X/Y graphing system. So essentially, the Y-intercept is when X=0. To find this, we simply plug zero in for the variable 'X':
0 + 3y = 3
Simplified
3y = 3
Divided
y = 1
So your Y-intercept is Y = 1
Hope this helps.
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