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Write an equation in slope-intercept form of the line.

Write an equation in slope-intercept form of the line.-example-1
User David Ham
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1 Answer

3 votes

Answer:

y = -1/3x +3

Explanation:

You want the slope-intercept equation of the line on the graph that has y-intercept 3 and x-intercept 9.

Slope

The slope of the line is the ratio of "rise" to "run". Here, the line decreases from a y-value of 3 to y=0 as the line goes from x=0 to x=9. The "rise" is -3 for a "run" of 9, so the slope is ...

m = rise/run = -3/9 = -1/3

Y-intercept

The line is seen to cross the y-axis at y=3. That is the y-intercept: b = 3.

Equation

The slope-intercept equation is ...

y = mx +b . . . . . . . where m is the slope and b is the y-intercept

y = -1/3x +3 . . . . equation of the graphed line

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Additional comment

Another way to get there is to use the intercept form of the equation:

x/a +y/b = 1 . . . . . . . . line with x-intercept 'a' and y-intercept 'b'

x/9 +y/3 = 1 . . . . . . . . using the intercept values from the graph

Solving for y gives the slope-intercept form of the equation.

1/3x +y = 3 . . . . multiply by 3

y = -1/3x +3 . . . . subtract 1/3x. This is the slope-intercept form.

User Rafal Borowiec
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5.8k points