Question

Quick algebra 1 question for 10 points!

Answer 1

Answer:

○ $3x + 4y = 7$

Step-by-step explanation:

The general form of the equation of a straight line is as follows:

$\boxed{y = mx + c}$,

where:

m = slope

c = y-intercept.

This means that m, which is the coefficient of $x$, needs to be $-\frac{3}{4}$.

Therefore we have to rearrange each equation given to make y the subject, and then check if the coefficient of $x$ becomes $-\frac{3}{4}$.

• First option:

$4x - 3y = 7$

⇒ $-3y = -4x + 7$

⇒ $y = \frac{4}{3}x -{ \frac{7}{3}$

∴ 'm' is $\bf \frac{4}{3}$, not  $-\frac{3}{4}$, therefore this option is incorrect.

• Second option:

$4x + 3y = 7$

⇒ $3y = -4x + 7$

⇒ $y = -\frac{4}{3}x + \frac{7}{3}$

∴ 'm' is $\bf -\frac{4}{3}$, not  $-\frac{3}{4}$, therefore this option is incorrect.

• Third option:

$3x + 4y = 7$

⇒ $4y = -3x + 7$

⇒ $y = -\frac{3}{4}x + \frac{7}{3}$

'm' is $\bf -\frac{3}{4}$, therefore this option is correct.

Note:

You can rearrange the equation given in the last option, and see that 'm' comes out to be $\frac{3}{4}$, thereby making it incorrect.

Answer 2

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

Given:

$\sf{- \dfrac{3}{4}}$

First, we take all the given options to their slope-intercept form:

$\longrightarrow \sf{y=m x+b}$

Taking to each equation to its slope-intercept form, you get:

$\small\longrightarrow \sf{-3y = 7 - 4x}$

$\small\longrightarrow \sf{- \dfrac{4}{ - 3} x + \dfrac{7}{3} }$

$\small\longrightarrow \sf{y = \dfrac{4}{ 3} x - \dfrac{7}{3} }$

$\small\longrightarrow \sf{3y = 7 - 4x}$

$\small\longrightarrow \sf{y = \dfrac{7}{3} - \dfrac{4}{3} x}$

$\small\longrightarrow \sf{4y y = = 7- 3x}$

$\small\longrightarrow \sf{y = \dfrac{7}{4} - \dfrac{3}{4} x}$

$\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}$

◉ $\bm{3x+4y=7}$