Write the equation of the line that passes through the give points (-4,-2) and (-3,5)

Answer 1

To find the equation of the line that passes through the points (-4, -2) and (-3, 5), first, you need to calculate the slope (m) of the line using the formula:

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

Here (x1, y1) = (-4, -2) and (x2, y2) = (-3, 5). Plugging these values into the formula gives:

m = (5 - (-2)) / (-3 - (-4))
m = (5 + 2) / (-3 + 4)
m = 7 / 1
m = 7

Now that you have the slope, you can use the point-slope form of the line equation, which is:

y - y1 = m(x - x1)

Using either one of the given points and the calculated slope, the equation becomes:

y - (-2) = 7(x - (-4))
y + 2 = 7(x + 4)

Now, if you want the equation in slope-intercept form (y = mx + b), you would simplify and solve for y:

y = 7x + 7(4) - 2
y = 7x + 28 - 2
y = 7x + 26

So, the equation of the line in slope-intercept form is:

y = 7x + 26

And that's the equation of the line that passes through the points (-4,-2) and (-3,5).