# Gradient intercept form: y = mx + b

## What is slope intercept form

Straight lines can be expressed in several form. Examples of some forms that express straight lines includes the point slope form or the general form. Today we’ll be learning about the slope intercept form.

You’ll recognize the slope intercept form of straight lines to be expressed in this format:

y = mx + b

## Find the slope and y intercept

### How to find the slope of an equation

Now that you know what the slope-intercept form looks like, what does it actually mean? You can actually tell the slope and the y intercept directly from the equation! In a slope intercept form equation, the “m” equals the slope of the line.

### how to find y intercept

So how about the y intercept? The “b” gives you the y intercept. Just from glancing at the equation gives you a lot of information you can use.

## Example problems

Question 1:

Determine the Slope-Y-int form from the graph.

Solution:

We are looking for an equation in this form: y=mx+b (the Slope-Y-int form).

From the graph, we can determine that the y-intercept = b = 4.

Next, we’ll find slope “m” using the rise over run method.

$m=\frac{3}{3}=1$

With the y-intercept and slope found, we can write out the equation:

y=x+4

Question 2:

Determine the slope and Y-intercept of the following linear function.

$4x-15=0$

Solution:

First, solve for x:

$4x=15$

$x=\frac{15}{4}$

Graphing out the equation will help us find the m and y-intercept.

It is a vertical line, so we’ve got an undefined slope. But why? Remember slope = rise over run.

Since it is a vertical line, nothing runs across the x axis. So the equation will look like this: m = \frac{#}{0}. Anything divided by 0 is undefined. Therefore, the slope of a vertical line is undefined.

Also, the line doesn’t intercept with the y axis at all. So there is no y-intercept.

Question 3:

A point (2,6) passes through an equation of $y=-5x+b$. Find “b”.

Solution:

(2,6) is a coordinate. It represents x=2 and y=6. So, to solve “b”, we can put the x and y value into the equation we are given:

$(6)=-5(2)+b$

$6=-10+b$

$16=b$

Put $16=b$ into the equation and we’ll get the complete slope intercept form equation:

$y=-5x+15$

Question 4:

Given two points through a line, find the slope-intercept form:

(-6,1) & (2,6)

Solution:

We are given two points. It allows us to solve for m using the slope equation that looks at the distances between the two points: m=y2-y1/x2-x1

$m=\frac{y_2-y_1}{x_2-x_1} = \frac{(6)-(1)}{(2)-(-6)}$

$m=\frac{5}{8}$

To solve for b, we pick either of the given points, along with m, and put them into y=mx+b:

$(6)=(\frac{5}{8})+b$

$6=\frac{10}{8}+b$

$b=4.75$ or $4\frac{3}{4}$

So the final answer is $y=\frac{5}{8}x+4\frac{3}{4}$

You can use this online graph to see what slope intercept form lines look like when it’s graphed out.

Coming up, you’ll learn about perpendicular line equations, parallel line equations, and system of linear quadratic equations that’ll build off of what you learned in this lesson.

### Gradient intercept form: y = mx + b

The slope intercept form is used to find the y-intercept and the slope of a straight line. If you look closely, it is a linear function too; meaning the function can tell you its domain and range.