Solved on Jan 24, 2024

Find the slope-intercept form of the linear equation $-5x + 15y = -30$ .

STEP 1

Assumptions
1. We are given a linear equation in the form $-5x + 15y = -30$ .
2. We want to write the equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To write the equation in slope-intercept form, we need to solve for $y$ in terms of $x$ . We start by isolating the $y$ -term on one side of the equation.
$-5x + 15y = -30$

STEP 3

Add $5x$ to both sides of the equation to move the $x$ -term to the right side.
$15y = 5x - 30$

STEP 4

Now, divide every term by the coefficient of $y$ to solve for $y$ .
$\frac{15y}{15} = \frac{5x}{15} - \frac{30}{15}$

STEP 5

Simplify the equation by performing the division.
$y = \frac{1}{3}x - 2$

STEP 6

The equation is now in slope-intercept form, where the slope $m$ is $\frac{1}{3}$ and the y-intercept $b$ is $-2$ .
The slope-intercept form of the given equation is:
$y = \frac{1}{3}x - 2$

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Find the slope-intercept form of the linear equation $-5x + 15y = -30$ .

STEP 1

Assumptions
1. We are given a linear equation in the form $-5x + 15y = -30$ .
2. We want to write the equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

To write the equation in slope-intercept form, we need to solve for $y$ in terms of $x$ . We start by isolating the $y$ -term on one side of the equation.
$-5x + 15y = -30$

STEP 3

Add $5x$ to both sides of the equation to move the $x$ -term to the right side.
$15y = 5x - 30$

STEP 4

Now, divide every term by the coefficient of $y$ to solve for $y$ .
$\frac{15y}{15} = \frac{5x}{15} - \frac{30}{15}$

STEP 5

Simplify the equation by performing the division.
$y = \frac{1}{3}x - 2$

STEP 6

The equation is now in slope-intercept form, where the slope $m$ is $\frac{1}{3}$ and the y-intercept $b$ is $-2$ .
The slope-intercept form of the given equation is:
$y = \frac{1}{3}x - 2$

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Find the slope-intercept form of the linear equation −5x+15y=−30-5x + 15y = -30−5x+15y=−30.

STEP 1

Assumptions1. We are given a linear equation in the form −5x+15y=−30-5x + 15y = -30−5x+15y=−30.2. We want to write the equation in slope-intercept form, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 2

To write the equation in slope-intercept form, we need to solve for yyy in terms of xxx. We start by isolating the yyy-term on one side of the equation.−5x+15y=−30-5x + 15y = -30−5x+15y=−30

STEP 3

Add 5x5x5x to both sides of the equation to move the xxx-term to the right side.15y=5x−3015y = 5x - 3015y=5x−30

STEP 4

Now, divide every term by the coefficient of yyy to solve for yyy.15y15=5x15−3015\frac{15y}{15} = \frac{5x}{15} - \frac{30}{15}1515y​=155x​−1530​

STEP 5

Simplify the equation by performing the division.y=13x−2y = \frac{1}{3}x - 2y=31​x−2

STEP 6

The equation is now in slope-intercept form, where the slope mmm is 13\frac{1}{3}31​ and the y-intercept bbb is −2-2−2.The slope-intercept form of the given equation is:y=13x−2y = \frac{1}{3}x - 2y=31​x−2

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the slope-intercept form of the linear equation $-5x + 15y = -30$ .

Assumptions
1. We are given a linear equation in the form $-5x + 15y = -30$ .
2. We want to write the equation in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

To write the equation in slope-intercept form, we need to solve for $y$ in terms of $x$ . We start by isolating the $y$ -term on one side of the equation.
$-5x + 15y = -30$

Add $5x$ to both sides of the equation to move the $x$ -term to the right side.
$15y = 5x - 30$

Now, divide every term by the coefficient of $y$ to solve for $y$ .
$\frac{15y}{15} = \frac{5x}{15} - \frac{30}{15}$

Simplify the equation by performing the division.
$y = \frac{1}{3}x - 2$

The equation is now in slope-intercept form, where the slope $m$ is $\frac{1}{3}$ and the y-intercept $b$ is $-2$ .
The slope-intercept form of the given equation is:
$y = \frac{1}{3}x - 2$