Question

(3,-2); slope 13

write an equation of the line that passes through the given point and has the given slope.​

Answer 1

y = 13x - 41

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 = 13 , then

y = 13x + c ← is the partial equation

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

- 2 = 13(3) + c = 39 + c ( subtract 39 from both sides )

- 41 = c

y = 13x - 41 ← equation of line

Answer 2

y = 13x - 41 is the final equation of the line with a slope of 13 that passes through the point (3, -2).

Step-by-step explanation:

To write an equation of the line that passes through the given point (3, -2) and has the given slope of 13, we use the point-slope formula of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.

Plugging our values into the formula we get:

y + 2 = 13(x - 3)

This can be simplified to get the equation in slope-intercept form:

y = 13x - 39 - 2

y = 13x - 41

This is the final equation of the line with a slope of 13 that passes through the point (3, -2).