Question

Use the information given to enter an equation in standard form.

Slope is 2/7 and (3, 1) is on the line.
a) 7x - 2y = 11
b) 2x - 7y = 11
c) 7x - 2y = 1
d) 2x - 7y = 1

Answer 1

To write the equation with a slope of 2/7 and through the point (3,1) in standard form, we start with the slope-intercept form y = mx + b, solve for b, and then manipulate the equation to standard form, yielding 7x - 2y = 1.

Step-by-step explanation:

The student's question asks how to write an equation of a line in standard form given the slope and a point on the line. The given slope is ⅗ and the point is (3, 1). To find the standard form, one approach is to first write the equation in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

To begin, we plug in the slope (⅗) and the coordinates of the given point to solve for b:

1 = (⅗)(3) + b

1 = ​⅖ + b

b = 1 - ​⅖

b = ​⅗

Now, the slope-intercept form of the equation is y = ⅗x + ⅗. To convert this to standard form, we multiply every term by 7 to eliminate the fractions:

7y = 2x + 1

Then, we rearrange the terms to get everything on one side:

2x - 7y = -1

However, we prefer the coefficients to be positive in standard form, so we multiply by -1:

-2x + 7y = 1 (This is not the final standard form. We multiply by -1 for positivity)

Therefore, the final equation in standard form is:

7x - 2y = 1