The general equation of a line in slope intercept form is:-
y = mx + c
where, m = slope of the line and c = y-intercept of the line
Now, the given equation of the line is :-
2x + 3y - 9 = 0
or, 3y = -2x + 9
Dividing both sides by 3, we get:
y = -(2/3)x + 3
Comparing the above equation with the general equation of the slope intercept form, we get
m = -(2/3) & c = 3
An equation of a line in the form y = mx + c is said to be in the slope y-intercept form. In a equation like this, 'm' represents the slope of the line, and c represent y-intercept of line, which is same as the y coordinate of the line where it intercepts the x-axis.
The given equation is:
2x + 3y - 9 = 0
It can be converted into the intercept form in the following steps:
3y = - 2x + 9
y = (-2/3)x + 9/3
y = (-2/3)x + 3
The above is the equation of line is in slope y-intercept form. In this equation value of m = -2/3, and value of c = 3.
Slope of the line = m = -2/3
y-intercept of the line = c = 3
First off, you need to know what the slope y-intercept form is. Basically, the form allows you to quickly see the y-intercept (where the line crosses the y-axis) and the slope (how sharp or shallow the line is). The form is shown as y = mx + b, where "m" is the slope and "b" is the y-intercept. Next, you need to rearrange the equation you were given, so you can have it in the proper form (y=mx+b). The steps are as follows: [step 1] 2x + 3y - 9 = 0; [step 2] 2x + 3y - 9 + 9 = 0 + 9 (add 9 to both sides to simplify non-variable terms); [step 3] 2x + 3y = 9; [step 4] 2x - 2x + 3y = 9 - 2x (subtract 2x from both sides to separate variable terms); [step 5] 3y = 9 - 2x; [step 6] 3y/3 = (9 - 2x)/3 (divide both sides by 3 to get y by itself); [step 7] 3y/3 = 9/3 -2x/3 (distribute division by 3); [step 8] y = 3 - (2/3)x; [step 10] y = (-2/3)x + 3 (rearrange terms, to put into proper format). Lastly, now that you have converted the equation into the proper "slope y-intercept form", you can quickly pull out the information to identify the slope and y-intercept. y = mx + b m = slope; b = y-intercept y = (-2/3)x + 3 slope = -2/3; y-intercept = 3 This means that the line represented by y=(-2/3)x+3 will cross through the y-axis (vertical one) at positive 3, and will be sloping down from the upper left to the bottom right at a rate of going down 2 units for each 3 units it moves to the right.
The given equation 2x+3y-9 =0 could be rearranged by adding -2y+9 to both sides and written like:
3y = -2x+9 . Diving by 3 both sides,
y = (-2/3)x+3. This is the slope intercept form of the line. The slope is (-2/3) , the coefficient of x in this form and +3 is the y intercept.
Also you can write y= mx+c. Here m is the slope. What is it? m = (y-c)/x, Or m = (y2-y1)/(x2-x1) is the rate oat which y increases or decreases per unit of increase in x units. And c is the value you get through the equation when you put x =0.
Remember that the formula for slope intercept is:
y = mx + b
where m is the slope and b is the y-intercept.
You're equation is : 2x + 3y - 9 = 0
Its almost like the Standard form: Ax + By = C
To turn your almost standard form equation into slope intercept, just solve for y:
2x + 3y = 9
3y = -2x + 9
y = `(-2x)/(3) + 3`