If we have two points, we can find the slope of the line between them by using the definition of the slope:

$\displaystyle slope = \frac{\Delta Y}{\Delta X}$    where the triangle is the greek letter 'Delta', and is used as a symbol for 'difference' or 'change in'

Now that we have our slope ( $\displaystyle \frac{4}{2}$, simplified to $\displaystyle 2$), we can write the equation for slope-intercept form:

$\displaystyle y=mx+b$   where $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept

$\displaystyle y=2x+b$

In order to find the y-intercept, we simply plug in one of the points on our line

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

$\displaystyle 1=-2+b$

$\displaystyle b=3$

So our equation looks like    $\displaystyle y=2x+3$

Because we have the desired slope and the y-intercept, we can easily write this as an equation in slope-intercept form (y=mx+b).

This gives us $\displaystyle y=4x/3-5$. Because this does not match either of the answers in this form (y=mx+b), we must solve the equation for x. Adding 5 to each side gives us $\displaystyle y+5=4x/3$. We can then multiple both sides by 3 and divide both sides by 4, giving us $\displaystyle 3y/4+15/4=x$.

If the y-intercept of a line is $\displaystyle 5$, then the $\displaystyle y$-value is $\displaystyle 5$ when $\displaystyle x$ is zero. Write the point:

$\displaystyle (0,5)$

If the $\displaystyle x$-intercept of a line is $\displaystyle -1$, then the $\displaystyle x$-value is $\displaystyle -1$ when $\displaystyle y$ is zero. Write the point:

$\displaystyle (-1,0)$

Use the following formula for slope and the two points to determine the slope:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1} = \frac{0-5}{-1-0}= \frac{-5}{-1} =5$

Use the slope intercept form and one of the points, suppose $\displaystyle (0,5)$, to find the equation of the line by substituting in the values of the point and solving for $\displaystyle b$, the $\displaystyle y$-intercept.

$\displaystyle y=mx+b$

$\displaystyle 5=(5)(0)+b$

$\displaystyle b=5$

Therefore, the equation of this line is $\displaystyle y=5x+5$.

The slope intercept form can be written as:

$\displaystyle y=mx+b$

where $\displaystyle m$ is the slope and $\displaystyle b$ is the y-intercept. Plug in the values of the slope and $\displaystyle y$-intercept into the equation.

The correct answer is: $\displaystyle y=6x+6$

The $\displaystyle x$-intercept is the value of $\displaystyle x$ when the $\displaystyle y$ value is equal to zero. The actual point located on the graph for an $\displaystyle x$-intercept of $\displaystyle 2$ is $\displaystyle (2,0)$. The slope, $\displaystyle m$, is 2.

Write the slope-intercept equation and substitute the point and slope to solve for the $\displaystyle y$-intercept:

$\displaystyle y=mx+b$

$\displaystyle 0=2(2)+b$

$\displaystyle b=-4$

Plug the slope and $\displaystyle y$-intercept back in the slope-intercept formula:

$\displaystyle y=2x-4$

First, find the slope of the line using the slope formula: 

$\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{7-3}{3-2}=\frac{4}{1}=4$.

Next we plug one of the points, and the slope, into the point-intercept line forumula:

 $\displaystyle y=mx+b$ where m is our slope.

Then $\displaystyle y=4x+b$ and when we plug in point (2,3) the formula reads $\displaystyle 3=4(2)+b$ then solve for b. 

$\displaystyle 3-8=-5 =b$.

To find the equation of the line, we plug in our m and b into the slope-intercept equation.

So, $\displaystyle y=4x+(-5)$ or simplified, $\displaystyle y=4x-5$.

To determine the equation, first find the slope:

$\displaystyle \frac{\Delta y}{\Delta x} = \frac{3--1}{-4-4} = \frac{4 }{-8 } =- \frac{1}{2}$

We want this equation in slope-intercept form, $\displaystyle y = mx+b$. We know $\displaystyle x$ and $\displaystyle y$ because we have two coordinate pairs to choose from representing an $\displaystyle x$ and a $\displaystyle y$. We know $\displaystyle m$ because that represents the slope. We just need to solve for $\displaystyle b$, and then we can write the equation.

We can choose either point and get the correct answer. Let's choose $\displaystyle (4, -1)$: 

$\displaystyle -1 = -\frac{1}{2} (4) + b$ multiply "$\displaystyle mx$"

$\displaystyle -1 = -2 + b$ add $\displaystyle 2$ to both sides

$\displaystyle 1 = b$

This means that the $\displaystyle y = mx+b$ form is $\displaystyle y = -\frac{1}{2}x +1$

To determine the equation, first find the slope:

$\displaystyle \frac{\Delta y}{\Delta x} = \frac{3-2}{2--1} = \frac{1 }{3 }$

We want this equation in slope-intercept form, $\displaystyle y = mx+b$. We know $\displaystyle x$ and $\displaystyle y$ because we have two coordinate pairs to choose from representing an $\displaystyle x$ and a $\displaystyle y$. We know $\displaystyle m$ because that represents the slope. We just need to solve for $\displaystyle b$, and then we can write the equation.

We can choose either point and get the correct answer. Let's choose $\displaystyle (3,2)$: 

$\displaystyle 2= \frac{1}{3} (3) + b$ multiply "$\displaystyle mx$"

$\displaystyle 2 = 1 + b$ subtract $\displaystyle 1$ from both sides

$\displaystyle 1 = b$

This means that the $\displaystyle y = mx+b$ form is $\displaystyle y = \frac{1}{3}x +1$

To determine the equation, first find the slope:

$\displaystyle \frac{\Delta y}{\Delta x} = \frac{-7--1}{3-5} = \frac{-6 }{-2 } =3$

We want this equation in slope-intercept form, $\displaystyle y = mx+b$. We know $\displaystyle x$ and $\displaystyle y$ because we have two coordinate pairs to choose from representing an $\displaystyle x$ and a $\displaystyle y$ . We know $\displaystyle m$ because that represents the slope. We just need to solve for $\displaystyle b$, and then we can write the equation.

We can choose either point and get the correct answer. Let's choose $\displaystyle (3, -7)$: 

$\displaystyle -7 = 3 (3) + b$ multiply "$\displaystyle mx$"

$\displaystyle -7 =9+ b$ subtract $\displaystyle 6$ from both sides

$\displaystyle -16 = b$

This means that the $\displaystyle y = mx+b$ form is $\displaystyle y = 3x -16$

To determine the equation, first find the slope:

$\displaystyle \frac{\Delta y}{\Delta x} = \frac{2--4}{6--3} = \frac{6}{9 } =\frac{2}{3}$

We want this equation in slope-intercept form, $\displaystyle y = mx+b$. We know $\displaystyle x$ and $\displaystyle y$ because we have two coordinate pairs to choose from representing an $\displaystyle x$ and a $\displaystyle y$. We know $\displaystyle m$ because that represents the slope. We just need to solve for $\displaystyle b$, and then we can write the equation.

We can choose either point and get the correct answer. Let's choose $\displaystyle (6, 2)$: 

$\displaystyle 2 = \frac{2}{3} (6) + b$ multiply "$\displaystyle mx$"

$\displaystyle 2 = 4 + b$ subtract $\displaystyle 4$ from both sides

$\displaystyle -2 = b$

This means that the $\displaystyle y = mx+b$ form is $\displaystyle y = \frac{2}{3}x-2$