Question

Write the equation of the line that passes through (-6, 1) and (4, -3)​

Answer 1

Answer: y = 5x + 31

Explanation:

You have to find the slope which is change in y over change in x. That would be (-6-4)/(1-3)

that simplifies down to 5.

You equation for a linear equation is y=mx+b with m=slope and b=y-intercept

Take a point and plug in the values for x and y. I'm going to use (-6, 1) but it doesn't really matter

1=5(-6)+b

1=-30+b

+30 +30

31 = b

Now you have everything for your equation so when you put it all together, it is y=5x+31

Answer 2

To find the equation of the line passing through two points, we need to use the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the given points.

First, we can find the slope of the line using the two points:

m = (y2 - y1) / (x2 - x1)

m = (-3 - 1) / (4 - (-6))

m = -4/10

m = -2/5

Now, we can use one of the points and the slope to write the equation of the line:

y - y1 = m(x - x1)

y - 1 = (-2/5)(x - (-6))

y - 1 = (-2/5)(x + 6)

y - 1 = (-2/5)x - (2/5) * 6

y - 1 = (-2/5)x - 12/5

y = (-2/5)x - 12/5 + 1

y = (-2/5)x - 12/5 + 5/5

y = (-2/5)x - 7/5

Therefore, the equation of the line that passes through (-6, 1) and (4, -3) is y = (-2/5)x - 7/5.