What is the equation of the line that passes through the point (−6,−5) and has a slope of -1/2

Answer 1

Hello, Alanna!

Whenever you are trying to find the equation of a linear function, you must consider what is given to you.

When you are given two points, you must find the slope using the slope formula and then use point-slope form.

When you are given one point and one slope, then you can immediately use point-slope form.

When you are given the slope and the y-intercept, you can immediately use slope-intercept form.

In this case, you are given a point and a slope, which means you will use point-slope form. You must have point-slope form memorized in order to finish the problem.

Point-slope form is (y-y₁) = m(x-x₁) where (x₁, y₁) are the coordinates to the point you are given and m = slope.

It is helpful to label your point as (x1, y1) before you even begin the problem so that you do not plug in the numbers into the incorrect places.

(-6,-5)

(x1,y1)

So, x1 = -6 and y1 = -5

Now we simply need to plug in everything and simplify.

y-(-5) = -1/2 (x-(-6))

y + 5 = -1/2(x+6)

y + 5 = -1/2x -3 (I distributed the -1/2 to the x and the 6)

-5 -5

y = -1/2x - 8 is your final answer

So try to memorize this pattern to help you for future problems

Given 2 points = find slope + use point-slope form

Given 1 point, 1 slope = use point-slope form

Given 1 slope, 1 y-intercept = use slope-intercept form

Answer 2

The general formula for a linear line is y=mx+b.

m is the slope and b is the y intercept

The problem says that m is -1/2 so the equation becomes y = (-1/2)x + b

Now, we need to find the y intercept. This can be doing by plugging in -6 for x and -5 for y because it is a point on the line.

-5 = (-1/2) * -6 +b

b = -8

so the equation is y = (-1/2)x -8