Question

What is the equation of the line shown in the graph? (-3,1) (2,-4)

Answer 1

The equation of the line passing through the points (-3,1) and (2,-4) is y = -x - 2.

Step-by-step explanation:

The equation of a straight line can be determined using two points on the line. Given the points (-3,1) and (2,-4), we can find the slope of the line using the formula:

slope = (change in y)/(change in x)

Substituting in the values, we get:

slope = (-4-1)/(2-(-3)) = -5/5 = -1

Since we have the slope and one point, we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

Substituting in the values for the point (-3,1) and the slope (-1), we get:

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

Simplifying, we get:

y - 1 = -1(x + 3)

y - 1 = -x - 3

y = -x - 2

Therefore the equation is y = -x - 2

Answer 2

x + y = -2

Step-by-step explanation:

The two primary equations to remember when dealing with graphing 2-variable equations are: ax + by = c (a & b are the x & y coefficients, respectively), and the other is y = mx + c (m = slope, x & y represent themselves). There is another equation to find the slope. If not already known, it's: ∆y/∆x {∆(aka Delta) = difference}. So, since that's all been established, we can proceed to calculate your question:

1) Find your slope: 1 - (-4) = 5 for your y-variable. And -3 - 2 = -5 for your x-variable. So your slope = 5/-5 = -1

2) Use the y = mx + c equation together with either set of (x,y) coordinates to get the equation 1 = (-1)(-3) + c. Which gives you c = -2

3) So, going back to the main equation to remember, the ax + by = c, use a one of your given sets of x,y coordinates and input your known values for x, y, & c to get: a(-3) + b(1) = (-2) and do the same with other set (these are just double-checks, coefficients are all equal to 1 anyways). So, you should arrive to the equation: x + y = -2