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

First solve for the slope of the line, m using y=mx+b

m = (y2 – y1) / (x2 – x1)

= (15 – 14) / (–5 –3)

= (1 )/( –8)

=–1/8

y = –(1/8)x + b

Now, choose one of the coordinates and solve for b:

14 = –(1/8)3 + b

14 = –3/8 + b

b = 14 + (3/8)

b = 14.375

y = –(1/8)x + 14.375

Our first step will be to determing the slope of the line that connects the given points.

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{2-3}=\frac{1}{-1}=-1$

Our slope will be $\displaystyle -1$. Using slope-intercept form, our equation will be $\displaystyle y=(-1)x+b$. Use one of the give points in this equation to solve for the y-intercept. We will use $\displaystyle \dpi{100} \small (2,6)$.

$\displaystyle 6=(-1)(2)+b$

$\displaystyle 6=-2+b$

$\displaystyle 8=b$

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

$\displaystyle y=(-1)x+8$

$\displaystyle y=-x+8$

This is our final answer.

The answer is $\displaystyle x^2+y=10$.

A line can only be represented in the form $\displaystyle x=z$ or $\displaystyle y=mx+b$, for appropriate constants $\displaystyle z$, $\displaystyle m$, and $\displaystyle b$. A graph must have an equation that can be put into one of these forms to be a line.

$\displaystyle x^2+y=10$ represents a parabola, not a line. Lines will never contain an $\displaystyle x^2$ term.

If we rearrange the second equation it is the same as the first equation. They are the same line.

Recall that to find the midpoint of two points $\displaystyle (a,b)$ and $\displaystyle (c,d)$, you use the equation:

$\displaystyle \left(\frac{a+c}{2},\frac{b+d}{2}\right)$.

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

$\displaystyle \left(\frac{4+a}{2},\frac{3+b}{2}\right)=(7,15)$

You merely need to solve each coordinate for its respective value.

$\displaystyle \frac{4+a}{2}=7$

$\displaystyle 4+a=14$

$\displaystyle a=10$

Then, for the y-coordinate:

$\displaystyle \frac{3+b}{2}=15$

$\displaystyle 3+b=30$

$\displaystyle b=27$

Therefore, our other point is: $\displaystyle (10,27)$