How do you write an equation given (-3,4), (1,-4)?

Question

Eva Adamson · Accepted Answer

Point-slope form: #y-4=-2(x+3)#
Slope-intercept form: #y=-2x-2# Assuming you mean a line that passes through these two points, use point-slope form: #y-y1=m(x-x1)# To find the slope, m, use the slope formula #m = (y2-y1)/(x2-x1)# (-3,4) and (1,-4): #m=(-4-4)/(1+3)# #m=-8/4=-2# Now, plug in the slope and either point into point-slope form: #y-4=-2(x+3)# To convert this to slope intercept form, isolate y and simplify: #y-4=-2x-6# #y=-2x-2#

Eva Adamson · Answer

undefined To write the equation of a line given two points (-3,4) and (1,-4), you can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one point on the line, and m is the slope of the line.

First, calculate the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substitute the coordinates (-3,4) and (1,-4) into the formula:

m = (-4 - 4) / (1 - (-3))
m = (-8) / (1 + 3)
m = -8 / 4
m = -2

Now that you have the slope (m) and one point (-3,4), substitute these values into the point-slope form:

y - 4 = -2(x - (-3))

Simplify:

y - 4 = -2(x + 3)

Now, distribute the -2:

y - 4 = -2x - 6

Finally, add 4 to both sides to isolate y:

y = -2x - 6 + 4
y = -2x - 2

So, the equation of the line is y = -2x - 2.