Writing Equations in Slope-Intercept Form

Slope – Intercept Form:  y = mx + b

m represents the slope

b represents the y-intercept

Writing equations using the Slope – Intercept Form  

You need 2 things – m (slope) and b. Let’s try some examples.

Example 1:  Write an equation in slope-intercept form of the line that has a slope of 3 and a y-intercept of 9.

So, m = 3 and b = 9. We plug into the slope-intercept form y = mx + b to get –

y = 3x + 9

Example 2:  Write an equation in slope-intercept form of the line where m= ½ and a y-intercept of  ³⁄₂.

So, m = ½ and b = ³⁄₂. We plug into the slope-intercept form y = mx + b to get –

y = ½x + ³⁄₂

Example 3: Find the slope and y-intercept of  y = 6x – 9.  Using the slope-intercept form y = mx + b, we know that

slope m= 6 and y-intercept b = -9 

Example 4: Find the slope and y-intercept of  2x + 3y = 15.  Rewrite the equation into slope-intercept form y = mx + b –

So, slope m=^-2⁄₃ and y-intercept b = 5 

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Aniruddha Pochimcherla

As a high school senior and co-founder of STEAMism and TimeforAI.com, Ani enjoys challenges and problem solving, technical subjects including Artificial Intelligence and Engineering Design, and collaborating with like-minded peers on events and hackathons. He has interned with the City of Austin, was a NASA High School Aerospace Scholar in 2019-2020 and is a Math tutor at Mathnasium. He has been blogging since 2nd grade and dabbles in web design and coding. He enjoys STEM subjects and teaching, so STEAMism is a great way for him to combine both.

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