How do you write an equation in slope-intercept form for a line with points (-3, 1) and (-2, -5)?

Solution:

Given points (-3, 1) and (-2, -5)

We know that slope intercept form is y = mx + c --- [a]

As the line passes through the points (-3, 1) and (-2, -5), they must satisfy the equation

As we have two unknown ‘m’ and ‘c’. We need to find the slope first

slope= m= y₂ - y₁/x₂ - x₁

m = -5 - 1 / -2 - (-3)

m = -6/-2 + 3

m = -6/1

Slope = m = -6

Now, substitute x = -3, y = 1 and m = -6 in [a]

1 = (-3)(-6) + c

1= 18 + c

c = 1 - 18

c = -17

Therefore, the equation of line is y = -6x - 17

Summary:

The equation in slope-intercept form for a line with points (-3, 1) and (-2, -5) is y = -6x - 17.