Question

(with solution)

1.in the linear equation, m= 6 and b= -2, what is the equation in the slope intercept form
2.the line has a x-intercept of -2 and an y-intercept of 5. what is the equation of the line express in standard form
3.the line passes through the point (6,-13) and (-4,-3), what is the equation of the line express in standard form​

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and c the y- intercept )

(1)

Here m = 6 and b = - 2, then

y = 6x - 2

(2)

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Here m = - 2 and b = 5, then

y = - 2x + 5 ← equation in slope- intercept form

Add 2x to both sides

2x + y = 5 ← equation in standard form

(3)

Calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (6, - 13) and (x₂, y₂ ) = (- 4, - 3)

m =
`(-3+13)/(-4-6)` =
`(10)/(-10)` = - 1 , then

y = - x + b ← is the partial equation

To find b substitute either of the 2 points into the partial equation

Using (- 4, - 3 ) , then

- 3 = 4 + b ⇒ b = - 3 - 4 = - 7

y = - x - 7 ← equation in slope- intercept form

Add x to both sides

x + y = - 7 ← equation in standard form