Question

write an equation of the line that passes through the givin point and has the givin slope (3,-2); slope 1/3

Answer 1

y =
`(1)/(3)` x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given slope m =
`(1)/(3)` , then

y =
`(1)/(3)` x + c ← is the partial equation

to find c, substitute (3, - 2 ) for x and y in the partial equation

- 2 =
`(1)/(3)` (3) + c = 1 + c ( subtract 1 from both sides )

- 3 = c

y =
`(1)/(3)` x - 3 ← equation of line

Answer 2

To find the equation of the line passing through the point (3, -2) with slope 1/3, we use the point-slope equation and determine the slope-intercept form to be y = (1/3)x - 3.

Step-by-step explanation:

To solve the mathematical problem completely, we'll write the equation of the line that passes through the given point (3, -2) with a given slope of 1/3 using the point-slope form of a linear equation. The general form of the point-slope equation is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.

In this case, our point (x1, y1) is (3, -2) and our slope m is 1/3. Substituting these values into the point-slope form, we get:

(y - (-2)) = (1/3)(x - 3)

Simplifying the equation, we add 2 to both sides:

y + 2 = (1/3)x - 1

Then we subtract 2 from both sides to write the equation of the line:

y = (1/3)x - 1 - 2

Finally, we have:

y = (1/3)x - 3

This is the equation of the line in slope-intercept form that satisfies the conditions of passing through the point (3, -2) with a slope of 1/3