1 more Linear Math Problem. (Find slope and y-intercept)

In summary, the conversation is about finding the slope and y-intercept of a line given an equation. The key is to make the coefficient of 'y' equal to 1 by dividing both sides of the equation by the same number. To find the y-intercept, set x to 0, and to find the x-intercept, set y to 0. The slope is the rate of change of the line, represented by 'a' in the equation y=ax + b.
  • #1
nukeman
655
0

Homework Statement



Find the slope m and y-intercept (0,b) of the line
2x + 4y =8

Homework Equations



I am still having troubles with finding the slope and y-intercept of a line.

Can you please solve this equation for me, but show me the steps, and break it down? It would really help. Include why you did that certain step.

The Attempt at a Solution



You guys are great. I really appreciate the great help!
 
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  • #2
2x + 4y =8

the key is to make the coefficient of 'y' equal to 1.

So what number should you divide by to make the coefficient of 'y' equal to 1?
 
  • #3
rock.freak667 said:
2x + 4y =8

the key is to make the coefficient of 'y' equal to 1.

So what number should you divide by to make the coefficient of 'y' equal to 1?

Is it 4 ?
 
  • #4
nukeman said:
Is it 4 ?

Right so divide by '4' and move the term in 'x' to the other side of the equation. What do you get?
 
  • #5
rock.freak667 said:
Right so divide by '4' and move the term in 'x' to the other side of the equation. What do you get?

can u clearify this for me?
 
  • #6
rock.freak667 said:
Right so divide by '4' and move the term in 'x' to the other side of the equation. What do you get?
nukeman said:
can u clearify this for me?
Personally, I would move the term with the x on the other side before dividing both sides by 4.

To the OP: you really need to be familiar with the properties of equality. For instance, in the subtraction property of equality you can subtract something from both sides:
[tex]\begin{aligned}
a + b &= c \\
a + b - b &= c - b \\
a &= c - b
\end{aligned}[/tex]

With the division property of equality, you can divide from both sides, as long as you're not dividing by zero:
[tex]\begin{aligned}
ab &= c \\
\frac{ab}{b} &= \frac{c}{b} \\
a &= \frac{c}{b} \\
\end{aligned}[/tex]
(b ≠ 0)

Now use these properties to solve for y in your equation.69
 
  • #7
First make your line into a known function of the form
l:y=ax + b

Finding the y-intersect set x to zero (b), finding the x-intersect set y to zero.
The slope is the rate at which your line changes vertically which is given by 'a'
 

1. How do I find the slope and y-intercept in a linear math problem?

To find the slope and y-intercept in a linear math problem, you can use the formula y = mx + b, where m represents the slope and b represents the y-intercept. The slope is the ratio of the change in y to the change in x, while the y-intercept is the value of y when x is equal to 0.

2. What is the significance of the slope and y-intercept in a linear math problem?

The slope and y-intercept are important values in a linear math problem because they help determine the equation of the line. The slope represents the rate of change of the line, while the y-intercept represents the starting point of the line. They also help in graphing the line and finding other important points on the line.

3. Can the slope or y-intercept be negative in a linear math problem?

Yes, both the slope and y-intercept can be negative in a linear math problem. A negative slope indicates a negative rate of change, while a negative y-intercept means the line intersects the y-axis below the origin.

4. What if the given linear math problem has more than two variables?

If the linear math problem has more than two variables, you will need to use a system of equations to find the slope and y-intercept. This involves solving for each variable in terms of the other variables and then using substitution to find the values of the slope and y-intercept.

5. Can the slope or y-intercept be fractions or decimals?

Yes, the slope and y-intercept can be fractions or decimals in a linear math problem. This is because slope is a ratio of two numbers and the y-intercept is a point on the coordinate plane, which can have non-integer values.

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