First you must figure out what point has an x-intercept of 3. This means the line crosses the x-axis at 3 and has no rise or fall on the y-axis which is equivalent to (3, 0). Now you use the formula (y₂ – y₁)/(x₂ – x₁) to determine the slope of the line which is (5 – 0)/(–2 – 3) or –1. Now substitute a point known on the line (such as (–2, 5) or (3, 0)) to determine the y-intercept of the equation y = –x + b. b = 3 so the entire equation is y = –x + 3.

If the square has a perimeter of 22, each side is 22/4 or 5.5.  This means that the upper-right corner is (2.75, 2.75)—remember that each side will be "split in half" by the x and y axes.

Using the two points we have, we can ascertain our line's equation by using the point-slope formula. Let us first get our slope:

m = rise/run = (2.75 – 5)/(2.75 + 1) = –2.25/3.75 = –(9/4)/(15/4) = –9/15 = –3/5.

The point-slope form is: y – y₀ = m(x – x₀). Based on our data this is: y – 5 = (–3/5)(x + 1); Simplifying, we get: y = (–3/5)x – (3/5) + 5; y = (–3/5)x + 22/5

Based on the information provided, you can find the slope of this line easily.  From that, you can use the point-slope form of the equation of a line to compute the line's full equation.  The slope is merely:

\(\displaystyle \frac{rise}{run}=\frac{17-(-11)}{-2-5}=\frac{17+11}{-7}=\frac{-28}{7}=-4\)

Now, for a point \(\displaystyle (a,b)\) and a slope \(\displaystyle m\), the point-slope form of a line is:

\(\displaystyle y-b=m(x-a)\)

Let's use \(\displaystyle (-2,17)\) for our point \(\displaystyle (a,b)\)

This gives us:

\(\displaystyle y-17=-4(x+2)\)

Now, distribute and solve for \(\displaystyle y\):

\(\displaystyle y-17=-4x-8\)

\(\displaystyle y=-4x+9\)

Based on the information provided, you can find the slope of this line easily.  From that, you can use the point-slope form of the equation of a line to compute the line's full equation.  The slope is merely:

\(\displaystyle \frac{rise}{run}=\frac{11-(-9)}{41-4}=\frac{11+9}{37}=\frac{20}{37}\)

Now, for a point \(\displaystyle (a,b)\) and a slope \(\displaystyle m\), the point-slope form of a line is:

\(\displaystyle y-b=m(x-a)\)

Let's use \(\displaystyle (4,-9)\) for our point \(\displaystyle (a,b)\)

This gives us:

\(\displaystyle y+9=\frac{20}{37}(x-4)\)

Now, distribute and solve for \(\displaystyle y\):

\(\displaystyle y+9=\frac{20}{37}x-\frac{80}{37}\)

\(\displaystyle y=\frac{20}{37}x-\frac{80}{37}-9\)

\(\displaystyle y=\frac{20}{37}x-\frac{80}{37}-\frac{333}{37}\)

\(\displaystyle y=\frac{20}{37}x-\frac{413}{37}\)

Based on the information that you have been provided, you can quickly find the slope of your line.  Since the y-intercept is \(\displaystyle 9\), you know that the line contains the point \(\displaystyle (0,9)\).  Therefore, the slope of the line is found:

\(\displaystyle \frac{-12-9}{4-0}=\frac{-21}{4}\)

Based on this information, you can use the standard slope-intercept form to find your equation:

\(\displaystyle y=mx+b\), where \(\displaystyle m=\frac{-21}{4}\) and \(\displaystyle b=9\)

\(\displaystyle y=\frac{-21}{4}x+9\)

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

P₁ (0, 6) and P₂ (4, 0)

First, calculate the slope:  m = rise ÷ run = (y₂ – y₁)/(x₂ – x₁), so m = –3/2

Second, plug the slope and one point into the slope-intercept formula: 

y = mx + b, so 0 = –3/2(4) + b and b = 6

Thus, y = –3/2x + 6

If P₁(1, 3) and P₂(3, 6), then calculate the slope by m = rise/run = (y₂ – y₁)/(x₂ – x₁) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

The slope intercept form states that \(\displaystyle \dpi{100} \small y=mx+b\). In order to convert the equation to the slope intercept form, isolate \(\displaystyle \dpi{100} \small y\) on the left side:

\(\displaystyle \dpi{100} \small 8x-2y=12\)

\(\displaystyle \dpi{100} \small -2y=-8x+12\)

\(\displaystyle \dpi{100} \small y=4x-6\)

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4