To write the equation of the line that goes through the points (4, -6) and (1, 2) in slope-intercept form, we can use the slope-intercept form of a linear equation: y = mx + b.

To find the slope of the line, we can use the formula:

m = (y2 – y1) / (x2 – x1)

Plugging in the values, we get:

m = (2 – (-6)) / (1 – 4)

= 8 / -3

= -2.67

The slope of the line is therefore -2.67.

Now that we know the slope of the line, we can use the point-slope form of a linear equation to find the equation of the line:

y – y1 = m(x – x1)

Plugging in the values, we get:

y – (-6) = (-2.67)(x – 4)

We can then simplify the equation by combining like terms:

y + 6 = -2.67x + 10.67

Finally, we can rewrite the equation in slope-intercept form by solving for y:

y = -2.67x + 16.67

So the equation of the line that goes through (4, -6) and (1, 2) in slope-intercept form is y = -2.67x + 16.67.

I hope this helps! Let me know if you have any questions.