Question

Find the equation of the line in slope-intercept form containing the two points: (−1,5) and )(4,−3) Leave equation in fractional form.

Answer 1

Answer:

y = 1.6x + 3.4

Step-by-step explanation:

We have to use the equation y = m x + c to find the equation of the line.

Here,

m ⇒ slope

c ⇒ y-intercept

First, let us find the slope.

For that, we can use the given two coordinates.

( -1 , 5 ) ⇒ ( x₁ , y₁ )

( 4 , -3 )  ⇒ ( x₂ , y₂ )

The formula to find the slope of a line is :

m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )

Let us solve now.

m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )

m = ( 5 - ( -3 ) ) ÷ ( -1 - 4 )

m = ( 5 + 3 ) ÷ -5

m = 8 ÷ -5

m = -1.6

Now let us find the y-intercept (c ) of the line.

For that, let us get one of the coordinates which are given in the question.

I'll get ( -1 , 5 ) from  that.

( -1 , 5 ) ⇒ ( x , y )

Let us solve now.

y = mx + c

5 = -1.6 × -1 + c

5 = 1.6 + c

5 - 1.6 = c

3.4 = c

Therefore,

m ⇒ -1.6

c ⇒ 3.4

So, the equation of the line is :

y = mx + c

y = 1.6x + 3.4