Question

How to write the equation of the line that goes through (4, –6) and (1, 2) answer in

Slope–Intercept Form.

Answer 1

Answer: y= -8/3x + 14/3

Explanation:

Slope–Intercept Form is y= mx + b

We see that the y increased by 8 and the x decreased by 3, so our slope is -8/3

The y-intercept is located at 14/3

So our answer is y= -8/3x + 14/3

Answer 2

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.