Question

Put the following equation of a line into slope-intercept form, simplifying all fractions. 4, x, plus, 5, y, equals, 20 4 � 5 � = 4x 5y= 20 20

Answer 1

To convert the equation 4x + 5y = 20 into slope-intercept form (y = mx + b), subtract 4x from both sides and then divide by 5 to isolate y, resulting in y = 4 - (4/5)x. This form reveals a slope of -(4/5) and a y-intercept of 4.

Step-by-step explanation:

To put the given equation, 4x + 5y = 20, into slope-intercept form, you need to solve for y. Slope-intercept form is expressed as y = mx + b, where m is the slope of the line and b is the y-intercept.

Here are the steps to rewrite the equation:

1. Subtract 4x from both sides of the equation: 5y = 20 - 4x.
2. Divide every term by 5 to solve for y: y = (20/5) - (4x/5).
3. Simplify the fractions: y = 4 - (4/5)x.

Now, the equation is in the form y = mx + b, with the slope m = -(4/5), and the y-intercept b = 4.

Answer 2

The equation 4x + 5y = 20 can be rearranged into slope-intercept form as
`\(y = -(4)/(5)x + 4\)`.

Step-by-step explanation:

Converting the given equation into slope-intercept form y = mx + b involves isolating y on one side of the equation. Start by moving the term with x to the other side by subtracting 4x from both sides of the equation 4x + 5y = 20.

4x + 5y = 20

5y = -4x + 20

To get y alone, divide each term by 5 to solve for y:

`\[y = -(4)/(5)x + (20)/(5)\]`

Simplify the equation:

`\[y = -(4)/(5)x + 4\]`

This equation is now in slope-intercept form y = mx + b, where m represents the slope of the line (-4/5) and b represents the y-intercept (4). Therefore, the equation of the line in slope-intercept form is
`\(y = -(4)/(5)x + 4\)`.

In this form, it's easy to identify the slope (-4/5) as the coefficient of \(x\) and the y-intercept (4), which represents the point where the line crosses the y-axis. This representation helps in understanding the characteristics of the line without performing additional calculations.