How to find a standard form equation for the line with slope 2/3 that passes through the point (3,6)?

poprskanvxcl

poprskanvxcl

Answered question

2023-02-27

How to find a standard form equation for the line with slope 2/3 that passes through the point (3,6)?

Answer & Explanation

koddann2hm9

koddann2hm9

Beginner2023-02-28Added 5 answers

The statement gives that m = 2 3 , so we have to find the value of b
Now, we also know that the line passes through ( 3 , 6 ) , and so:
6 = 2 3 3 + b and then 6 = 2 + b and so b = 4 . The equation of the line is then:
y = 2 3 x + 4
Idabuluq3xg

Idabuluq3xg

Beginner2023-03-01Added 6 answers

Finding the equation's slope-intercept form first, then changing it to standard form, is the first step.
The slope-intercept form is
y = m x + b
The slope m is given as 2 3 , so the equation up to that point is y = 2 3 x + b
Substitute the values for x and y from the ordered pair provided in the problem to determine b
6 = 2 3 ( 3 1 ) + b
Solve for b
1) Clear the parentheses by multiplying the fractions
6 = 2 + b
2) Subtract 2 from both sides to isolate b
4 = b
So the slope-intercept form of the equation is
y = ( 2 3 ) x + 4 slope-intercept form
The slope-intercept form should be changed to standard form.
Standard form is
a x + b y = c where a is a positive whole digit
1) Clear the fraction by multiplying all the terms on both sides by 3 and letting the denominator cancel
3 y = 2 x + 12
2) Subtract 2 x from both sides to get the x and y terms on the same side
- 2 x + 3 y = 12
3) Multiply through by - 1 to clear the minus sign
2 x - 3 y = - 12 standard form

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