How do you write an equation in slope intercept form for the line through the given point (5, -2) and (-16, 4)?

Answer 1
The slope of your line is: #m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)# and represents the inclination of your line (change in #y# for a change in #x#).
In your case you have: #m=(4-(-2))/(-16-5)=6/-21=-2/7#

you can now insert this slope into the relationship:

#y-y_0=m(x-x_0)# that gives the equation of your line using, for example, the coordinates of your first point as:
#y-(-2)=-2/7(x-5)#
giving: #y=(-2/7)x-(4/7)#
So you have a line of slope #m=-2/7# and intercept at #y=-4/7#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To write an equation in slope-intercept form for the line passing through the given points ((5, -2)) and ((-16, 4)), first find the slope (m) using the formula: [ m = \frac{y_2 - y_1}{x_2 - x_1} ] where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points. Substituting the given points: [ m = \frac{4 - (-2)}{-16 - 5} ] [ m = \frac{6}{-21} ] [ m = -\frac{2}{7} ]

Now that we have the slope (m), we can use one of the points (let's use ((5, -2))) and the slope to write the equation in slope-intercept form ((y = mx + b)). Substituting (m = -\frac{2}{7}) and the point ((5, -2)): [ -2 = -\frac{2}{7}(5) + b ] [ -2 = -\frac{10}{7} + b ] [ b = -2 + \frac{10}{7} ] [ b = -\frac{14}{7} + \frac{10}{7} ] [ b = -\frac{4}{7} ]

Therefore, the equation of the line in slope-intercept form is: [ y = -\frac{2}{7}x - \frac{4}{7} ]

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7