Equation of a Straight Line - Examples, Exercises and Solutions

In the first step, we'll find the slope using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

We'll substitute according to the given points:

$m=\frac{12-(-6)}{4-(-2)}$

$m=\frac{18}{6}=3$

Now we'll choose the point (4,12) and use the formula:

$y=mx+b$

$12=3\times4+b$

$12=12+b$

$b=0$

We'll substitute the data into the formula to find the equation of the line:

$y=3x$

In the first step, we'll find the slope using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

We'll substitute according to the given points:

$m=\frac{1-2}{\frac{1}{3}-(-\frac{1}{3})}$

$m=\frac{-1}{\frac{2}{3}}=-\frac{3}{2}$

Now we'll choose point $(\frac{1}{3},1)$ and use the formula:

$y=mx+b$

$1=-\frac{3}{2}\times\frac{1}{3}+b$

$1=-\frac{1}{2}+b$

$b=1\frac{1}{2}$

We'll substitute the given data into the formula to find the equation of the line:

$y=-\frac{3}{2}x+1\frac{1}{2}$

First, we will use the formula to find the slope of the straight line:

We replace the data and solve:

$\frac{(0-4.5)}{(5-0.5)}=\frac{-4.5}{4.5}=-1$

Now, we know that the slope is $-1$

We replace one of the points in the formula of the line equation:

$y=mx+b$

$(5,0)$

$0=-1\times5+b$

 $0=-5+b$

$b=5$

Now we have the data to complete the equation:

$y=-1\times x+5$

$y=-x+5$

First, write out the line equations:

$-4+y=5x-6$

$y=5x+4-6$

$y=5x-2$

From here we can determine the slope:

$m=5$

We'll use the formula:

$y=mx+b$

We'll use the point $(-2,-13)$:

$-13=5\times-2+b$

$-13=-10+b$

$-3=b$

Finally, substitute our data back into the formula:

$y=5x+(-3)$

$y=5x-3$

We will use the formula:

$m=\tan\alpha$

Let's check the slope of minus 6:

$-6=\tan\alpha$

$\tan^{-1}(-6)=\alpha$

$-80.53=\alpha$

$180-80.53=$

$99.47=\alpha_1$

Let's check the slope of one-half:

$\frac{1}{2}=\tan\alpha$

$\tan^{-1}(\frac{1}{2})=\alpha$

$26.56=\alpha_2$

\alpha_1 > \alpha_2