Complete the equation of the line through (-6,-5) and (-4,-4) Use exact numbers

Answer 1

The equation of a line is y = (m•x) + b

y - the y coordinate of a point on the line (usually your output)

m - the slope of the line

x - the x coordinate of a point on the line (usually your input)

b - the y intercept of the line (where the line crosses the y axis, when x = 0)

To calculate the slope, the formula is (y₂ - y₁) ÷ (x₂ - x₁). A general rule of thumb is the slope = rise ÷ run, or the change in y divided by the change in x between two points.

Here, we'll made (-6, -5) point 1 and (-4, -4) point 2. So, to solve for your slope, you would do:

(-4 - (-5)) ÷ (-4 - (-6))

This would evaluate to 1 ÷ 2, so your slope is 1/2 or 0.5. Now your equation is y = (1/2 • x) + b. To find b, simply pick one of your points, input the x and y values into their respective places in the equation, and solve for b. Here, let's pick point 2 to solve:

-4 = (1/2 • (-4)) + b

-4 = -2 + b

b = -2

So, your intercept is -2 and your final equation looks like this:

y = (1/2 • x) - 2

Answer 2

We will put this in y=mx +b form so first calculate the slope

m= (-4)-(-5)/(-4)-(-6)

m= 1/2. So y= x/2. +b

Now just substitute the x and y values of either given point to calculate b

I will use (-4,-4)

-4= (1/2)(-4) +b

-4= -2 +b

b=-2

So equation is y= x/2 -2

Answer 3

To determine any line (and thus its equation), we need to identify two elements: direction (otherwise known as slope) and position (usually in the form of a point). In this case, we can start by identifying the slope of the line intersecting these two points, using the slope formula. Slope is defined as the ratio of change in y to change in x, often stated as "rise over run". That is:

m = (y₂ - y₁)÷(x₂ - x₁).

In our case, for (x₁,y1) = (-6,-5) and (x₂,y₂) = (-4,-4), that works out to

m = (-4 - (-5))÷(-4 - (-6)) = 1/2.

Now that we know the slope of the line, we can construct an equation for the line in point-slope form, for which we'll choose a point (x₀,y₀) on the line and state that when we express the deviation of y from y₀ as (y - y₀) and the deviation of x from x₀ as (x - x₀), the ratio between the two will be equal to the slope:

(y - y₀)÷(x - x₀) = m,

or more commonly,

(y - y₀) = m•(x - x₀).

In our case, we'll just choose (x₀,y₀) to be one of the points we were already given - the point (-4,-4). Plugging in values, we obtain:

(y + 4) = 1/2•(x + 4).

This is the requested equation for the line between the two points. The only other consideration is that we may prefer to put the equation in slope-intercept form; this is easily done by solving the above equation for y and then simplifying:

y = 1/2•(x + 4) - 4

y = 1/2•x + 2 - 4

y = 1/2•x - 2.