Finding the equation of a straight line - Examples, Exercises and Solutions

Find the equation of the line passing through the two points $(5,0),(\frac{1}{2},4\frac{1}{2})$

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:

$y=-1\times x+5$

$y=-x+5$

$y+x=5$

Two lines have slopes of $-6$ and $\frac{1}{2}$.

Which of the lines forms a smaller angle with the x-axis?

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

The line with a slope of $\frac{1}{2}$

Find the equation of the line passing through the two points $(-2,-6),(4,12)$

$y=3x$

Find the equation of the line passing through the two points $(\frac{1}{3},1),(-\frac{1}{3},2)$

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

Find the equation of the line passing through the two points $(9,10),(99,100)$

$y=x+1$

Find the equation of the line passing through the two points $(2,8),(6,1)$

$y=-1\frac{3}{4}x+11\frac{1}{2}$

Find the equation of the line passing through the two points $(12,40),(2,10)$

$y-4=3x$

Find the equation of the line passing through the two points $(15,36),(5,16)$

$y=2x+6$

Find the equation of the line passing through the two points $(5,-11),(1,9)$

$y+5x=14$

Straight line passes through the point $(6,14)$ and parallel to the line $x+3y=4x+9$

$y=x+8$

Straight line passes through the point $(-2,-13)$ and parallel to the line $-4+y=5x-6$

$y=5x-3$

Straight line passes through the point $(-5,12)$ and parallel to the line $5y-5x=15$

$y-x=17$

Straight line passes through the point $(0,1)$ and parallel to the line $2(y+1)=16x$

$y-8x=1$

Two lines haves slopes of -3 and -6.

Which of the lines forms a greater angle with the x axis?

The line whose slope is -3 forms the greater angle.

Two straight lines have slopes of$2,\frac{1}{2}$.

Which of the lines forms a larger angle with the x axis?

The straight line with a slope of 2 forms the largest angle.