1. The slope of a line is 5 and its y-intercept is 8. Discuss how you will
write the equation in the slope-intercept form.
2. The profit P pesos from a buko juice stand can be modeled by the
equation
P = 5x - 100 where x represents the nurpber of glasses of buko juice
sold. What is the y-intercept? Explain what it represents in this
problem
3. Your classmate has been absent for the past few days. Write him/her a
letter describing how to convert an equation, such as y = 5 + 4(x - 5),
to slope-intercept form. Include examples in your explanation. End
your letter by telling your classmate how to identify equivalent
equations.
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Answer:
First, we must understand the slope-intercept form. The slope-intercept form is used to express an equation of a line. To use this, we only need to identify the a) slope of the line, b) the y-intercept of a line.
The slope-intercept form assumes the formula:
y = mx + b
• m is the slope of the line. A slope is the change in y over the change of x.
• b is the y-intercept. The y-intercept is where the line begins. The y-intercept lies on the y-axis where the line intercepts. Think of the y-intercept as a starting point.
1. y = 5x + 8
5 is the slope, and 8 is the y-intercept. Simply substitute the given in the formula.
2. - 100
The y-intercept represents the point where the line meets or intercepts with the y-axis.
3. y = 5 + 4 (x-5) ---> y = 4x - 15
• Distribute 4
y = 5+4(x-5)
y = 5+4x-20
• Combine like terms
y = 4x - 20 + 5
y = 4x - 15
Equivalent equations are algebraic expressions with the same roots. or solutions. It means the value of the roots or x for each equation are the same.
For example:
Is the equation "x + 3 = 5" and "2x + 3 = 7" equivalent equations?
• First find the roots.
x + 3 = 5
-3 = -3
x = 2
2x + 3 = 7
- 3 = -3
2x = 4
÷2 = ÷2
x = 2
Since both the equations have the same roots, therefore they are equivalent equations.