3. Express each of the following lines in the form $$ y=m x+c $$ and hence write down the slope of the line: $$ \begin{array}{lll} ext { (i) } x+y-4=0 & ext { (ii) } 3 x+y-5=0 & ext { (iii) } 2 x+3 y-7=0 \ ext { (iv) } 5 x-2 y+3=0 & ext { (v) } 3 x+4 y-2=0 & ext { (vi) } 3 x-4 y+6=0\end{array} $$

Question

3. Express each of the following lines in the form $$ y=m x+c $$ and hence write down the slope of the line: $$ \begin{array}{lll}	ext { (i) } x+y-4=0 & 	ext { (ii) } 3 x+y-5=0 & 	ext { (iii) } 2 x+3 y-7=0 \ 	ext { (iv) } 5 x-2 y+3=0 & 	ext { (v) } 3 x+4 y-2=0 & 	ext { (vi) } 3 x-4 y+6=0\end{array} $$

UpStudy AI · Accepted Answer

(i) Starting with  
$$
x+y-4=0
$$  
solve for $$ y $$:  
$$
y = -x+4.
$$  
The slope is $$ m=-1 $$.

(ii) Start with  
$$
3x+y-5=0.
$$  
Solve for $$ y $$:  
$$
y = -3x+5.
$$  
The slope is $$ m=-3 $$.

(iii) Given  
$$
2x+3y-7=0,
$$  
solve for $$ y $$:  
$$
3y = -2x+7 \quad \Longrightarrow \quad y = -\frac{2}{3}x+\frac{7}{3}.
$$  
The slope is $$ m=-\frac{2}{3} $$.

(iv) Given  
$$
5x-2y+3=0,
$$  
solve for $$ y $$:  
$$
-2y = -5x-3 \quad \Longrightarrow \quad y = \frac{5}{2}x+\frac{3}{2}.
$$  
The slope is $$ m=\frac{5}{2} $$.

(v) Given  
$$
3x+4y-2=0,
$$  
solve for $$ y $$:  
$$
4y = -3x+2 \quad \Longrightarrow \quad y = -\frac{3}{4}x+\frac{1}{2}.
$$  
The slope is $$ m=-\frac{3}{4} $$.

(vi) Given  
$$
3x-4y+6=0,
$$  
solve for $$ y $$:  
$$
-4y = -3x-6 \quad \Longrightarrow \quad y = \frac{3}{4}x+\frac{3}{2}.
$$  
The slope is $$ m=\frac{3}{4} $$.
Here are the equations in the form $$ y = mx + c $$ and their slopes: 1. $$ y = -x + 4 $$ → Slope $$ m = -1 $$ 2. $$ y = -3x + 5 $$ → Slope $$ m = -3 $$ 3. $$ y = -\frac{2}{3}x + \frac{7}{3} $$ → Slope $$ m = -\frac{2}{3} $$ 4. $$ y = \frac{5}{2}x + \frac{3}{2} $$ → Slope $$ m = \frac{5}{2} $$ 5. $$ y = -\frac{3}{4}x + \frac{1}{2} $$ → Slope $$ m = -\frac{3}{4} $$ 6. $$ y = \frac{3}{4}x + \frac{3}{2} $$ → Slope $$ m = \frac{3}{4} $$

Express each of the following lines in the form and hence write down the
slope of the line:

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Express each of the following lines in the form and hence write down the slope of the line: