# Write an Equation Given the Slope and a Point

## Key Questions

• The slope intercept formula is, $y = m x + b$

where $m$ is the slope
where $b$ is the $y$-intercept

The slope is the change in y over the change in x. This is commonly known as the $\frac{r i s e}{r u n}$. This is also shown as the $\frac{\Delta y}{\Delta x}$. If you have any 2 points on the line than you can also use the formula $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

The y-intercept is where the line touches or intersects the $y$-axis. If the $x$ coordinate is zero you can find out what the y-intercept is.

• What is x-intercept? It is such an argument (x-value) where y-value equals 0. In equations you would tell that it is root of the equation.

In general formula $y = m x + b$ you insert known information, where $m$ is a slope (or gradient) and $b$ is free-term (or y-intercept - such an value where function cuts y-axis, so point (0, b) ).

Let us take example. You are given slope - it is 2. And you know that your x-intercept is equal 3. Therefore, you know that when $x = 3$, $y = 0$.

Let us use that information. You know that you may write every linear function like that: $y = m x + b$.
Let us insert values: $0 = 2 \cdot 3 + b$
Our unknown is $b$, free term. Let us isolate it:
$b = - 6$.
And after all, we must insert our $b$ value back into equation: $y = 2 x - 6$.

• No, it does not matter since you will end up with an equivalent equation.

I hope that this was helpful.

• Slope Intercept form is y = mx + b, where
m = the slope and b = the y- intercept.

Slope is determined by formula

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

if you had the coordinates of two points on the line.

$\left({x}_{1} , {y}_{1}\right) \left({x}_{2} , {y}_{2}\right)$

b is the point at which the line will cross (intercept) the y-axis.

If a problem asked for the slope intercept form and provides a slope and a single point on the line you could find the equation with two different methods.

What is the slope intercept equation of a line with a slope of m = 3/4 and a point on the line of (4 , 5)?

The first method is to us the slope-intercept equation and plug in values to solve for b.

5 = $\frac{3}{4}$(4) + b (simplify the fraction)

5 = 3 + b (isolate b)

5 - 3 = b (simplify)

b = 2

The slope-intecept equation would be y = $\frac{3}{4}$x + 2

The second method is to use the point-slope formula

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

Plug in the information and simplify for the equation.

$\left(y - 5\right) = \frac{3}{4} \left(x - 4\right)$ (distribute the slope)

$\left(y - 5\right) = \frac{3}{4} x - 3$ (isolate y)

$y = \frac{3}{4} x - 3 + 5$ (simplify)

$y = \frac{3}{4} x + 2$ is the slope-intercept equation.