Find the equation of the line that passes through (-3,5) and (4,2).

Answer 1

Use two-point form:

(y - 5) / (x +3) = (7 - 5) / (4 + 3)

Answer 2

Using the "slope-intercept" format,we can set up 2 equations, using the given points.

The format: y = mx + b, where m is the slope and b is the y-intercept (where x = 0)

To find m and b, we need 2 equations which we get using the 2 given points:

(-3,5):

5 = m(-3) + b (equation 1)

(4,2):

2 = m(4) + b (equation 2)

Subtract #2 from #1 to get:

3 = -7m

m = -3/7

Then, using equation 1, find b:

5 = (-3/7)*(-3) + b

b = 5 - 9/7 = 26/7

The equation is then:

y = -3x/7 + 26/7

CHECK: (-3,5)---> if x = -3, y should be 5:

y = -3*-3/7 + 26/7 = 35/7 = 5

Answer 3

The line equation has the form y = mx + b

Where b the point in the y axis where the line crosses it (at x= 0) and m is the slope of the line as the values of x increase.

Having two points allows us to find the slope: how much does y change for a unit change in x. From -3 to 4, x changes 7, while y has gone from 5 to 2. That is a negative change of -3 (the slope is downward) and it is:

m = (-3/7).

To find the value of "b" (otherwise knows as the y-axis intercept), we can calculate the value of y as the line moves from either of the 2 points we already have, to the axis (or x=0).

Let's use the (-3,5), for example. The value of y is going to drop from 5, with a slope of -3/7 when we move from -3 to 0, by an amount equal to 3×(-3/7). That means that b = 5−(9/7) = 3.7143

So this line equation is y = (-3/7)x + 3.7143