Slope-intercept form: write an equation from a graph
Key Notes:
The slope-intercept form of a linear equation is
y = mx + b
where m is the slope and b is the y-intercept.
The slope formula is m= change in y/change in x
Learn with an example
Look at this graph
What is the equation of the line in slope-intercept form?
solution:
First, find the slope m. Pick two points on the line, such as (0, 3) and (7, 4). Plug those points into the slope formula.
m= change in y/change in x
m = 4-3/7-0
m = 1/7
The slope is =1/7
Now find the y-intercept. Since the line crosses the y-axis at 3, the y-intercept is 3.
Finally, use the slope m =1/7 and the y-intercept b = 3 to write the equation in slope-intercept form.
y = mx + b
y =1/7x + 3
Look at this graph.
What is the equation of the line in slope-intercept form?
First find the slope m. Pick two points on the line, such as (0, -2) and (1, 0). Plug those points into the slope formula.
m = change in y / change in x
m = 0 – -2 / 1 – 0 Plugin (0, -2) and (1, 0)
m = 2/1 Simplify
m = 2 Simplify
The slope is 2.
Now find the y-intercept. Since the line crosses the y-axis at -2, the y-intercept is -2.
Finally, use the slope m = 2 and the y-intercept b = 2 to write the equation in slope-intercept form.
y = mx + b
y = 2x + –2 Plugin m=2 and b = –2
y = 2x − 2 Rewrite as subtraction
Look at this graph.
What is the equation of the line in slope-intercept form?
First find the slope m. Pick two points on the line, such as (0, 10) and (1, 5). Plug those points into the slope formula.
m =change in y/ change in x
m =5 − 10 /1 − 0 Plugin (0, 10) and (1, 5)
m =–5/1 Simplify
m = –5 Simplify
Theslopeis–5.
Now find the y-intercept. Since the line crosses the y-axis at 10, the y-intercept is 10.
Finally,usetheslopem = –5andthey-interceptb = 10towritetheequationinslope-interceptform.
y = mx + b
y = –5x + 10 Plugin m = –5 and b = 10
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