Answer:
Explanation:
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.