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

2 Answers
Mar 26, 2018

You may use the standard form of the straight line:

y=mx+b, where m is the slope and b the y-intercept

Explanation:

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

Mar 26, 2018

The standard form is 2x - 3y = - 12

Explanation:

Start by finding the slope-intercept form of the equation, then converting that to the standard form.

The slope-intercept form is
y = mx + b

The slope m is given as 2/3, so the equation up to that point is
y = (2)/(3)x + b

To find b, sub in the values for x and y from the ordered pair given in the problem.

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 larr slope-intercept form

Change the slope-intercept form into standard form.

Standard form is
ax + by = 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
3y = 2x + 12

2) Subtract 2x from both sides to get the x and y terms on the same side
- 2x + 3y = 12

3) Multiply through by -1 to clear the minus sign
2x - 3y = - 12 larr standard form