Question

Write each equation in slope-intercept form. underline the slope and circle the y-intercept in each equation 5x+3y=30

Answer 1

Answer:

The slope is

5

3

.

The y-intercept is

−

10

.

Explanation:

5

x

−

3

y

=

30

is the standard form for a linear equation. The slope-intercept form is

y

=

m

x

+

b

, where

m

is the slope, and

b

is the y-intercept. To convert from standard form to slope-intercept form, solve the standard form for

y

.

5

x

−

3

y

=

30

Subtract

5

x

from both sides of the equation.

−

3

y

=

30

−

5

x

Divide both sides by

−

3

.

y

=

30

−

3

−

5

x

−

3

=

y

=

−

10

+

5

3

x

Rearrange the right hand side.

y

=

5

3

x

−

10

m

=

5

3

,

b

=

−

10

graph{y=5/3x-10 [-10, 10, -5, 5]}

Answer 2

Hi there!  

»»————-　★　————-««

I believe your answer is:  

$y = \underline{-\frac{5}{3}}x + \boxed{10}$

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

$\text{Converting to Slope-Intercept Form:}\\5x + 3y = 30\\\rule{150}{0.5}\\\rightarrow 5x - 5x + 3y = 30 - 5x\\\\\rightarrow 3y = 30-5x\\\\\rightarrow\frac{3y=30-5x}{3}\\\\\rightarrow y = 10 -\frac{5}{3}x\\\\\rightarrow \boxed{y = -\frac{5}{3}x + 10}$

⸻⸻⸻⸻

$\text{General Slope-Intercept Formula:}\\y = mx + b\\\rule{150}{0.5}\\ \bullet \text{ }m -\text{Slope}\\ \bullet \text{ }b -\text{Y-Intercept}\\\rule{150}{0.5}\\\text{In the given equation, the slope would be } -\frac{5}{3} \text{ and the y-intercept would be } 10.$

⸻⸻⸻⸻

$y = \underline{-\frac{5}{3}}x + \boxed{10}$

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.