Question

PLEASE HELP ASAP!

A line is drawn so that it passes through the points (-3,-1) and (4,2).

a. What is the slope of the line?

b. Using the point (4,2) and the slope found above, write the equation of the line in point-slope form.

Please write out how you got your answer or the steps you took.

Answer 1

A) To find slope, use the equation:
`slope = ( y_(2) - y_(1) )/(x_(2)-x_(1))`where
`x_(2)` and
`y_(2)` are the x and y values of one coordinate point , and
`x_(1)` and
`y_(1)` are the x and y values of another coordinate point . Since we are given two coordinate points, (-3,-1) and (4,2), that means we can find the slope using the slope equation.
Let's choose (4, 2) as your
`(x_(2), y_(2))` point and (-3, -1) as your
`(x_(1), y_(1))` point, but you can switch those if you want! That makes
`x_(2) = 4, y_(2) = 2` and
`x_(1) = -3, y_(1) = -1`. Plug these values into the slope equation:

`slope = ( y_(2) - y_(1) )/(x_(2)-x_(1)) \\ slope = (2-(-1))/(4-(-3)) \\ slope = (3)/(7)`

The slope of the line is 3/7.

B) Remember that the general equation for point-slope form is
`y - y_1 = m(x - x_1)`, where m = the slope,
`x_(1)` = the x value of a coordinate point
`(x_(1), y_(2))` on the line, and
`y_(1)` = the y value of the same coordinate point on the line.

You are given (4, 2) as one of the coordinate points. That means
`x_(1)` = 4 and
`y_(1)` = 2. We found the slope, m =
`(3)/(7)` in part A. Now plug these values into the general equation for point-slope form to find your point-slope form equation:

`y - y_1 = m(x - x_1)\\ y - 2 = (3)/(7)(x - 4)`

Your point-slope form equation is
`y - 2 = (3)/(7)(x - 4)`.