Question

1.The slope of a line is -4, and the y-intercept is -3. What is the equation of the line written in slope-intercept form?

y = -4x - 3
y = -4x + 3
y = 4x - 3

2.The graph of a line passes through the two points (-2, 1) and (2, 1). What is the equation of the line written in general form?
y - 1 = 0
x - y + 1 = 0
x + y - 1= 0

3.The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?
10x + 3y - 1 = 0
x + 3y + 10 = 0
x + 3y - 10 = 0

4.Write the equation of the line that has an x-intercept of -3 and passes through the point (-3, 7).

x = -3
y = -3
y = 7

Answer 1

ANSWER TO QUESTION 1

The equation of a line in slope intercept form is given by the formula,


`y = mx + c`
where

`m`
is the slope of the straight line and

`c`
is the y-value of the y-intercept.

It was given in the question that, the slope is -4.

Thus,


`m = - 4`

It was also given that the y-intercept is -3.

Thus,


`c = - 3`

Therefore the equation is


`y = - 4x + - 3`

This gives us,


`y = - 4x - 3`

The correct answer is A

ANSWER TO QUESTION 2

We were given that the equation passes through the two points (-2,1) and (2,1).

We can see from the points that the y-values are constant. This means that the line is parallel to the x-axis

Therefore the equation is given by


`y=y_1`
where

`y_1`
is the constant y-value.

Thus, the equation is,


`y = 1`

or we write in general form to get,


`y - 1 = 0`

The correct answer is A.

We could have also decided to find the slope,


`m = ( 1 - 1)/(2 - - 2) = (0)/(4) = 0`

using any point, say

`(2,1)`

we plug into the point slope form formula to get,


`y - 1 = 0(x - - 2)`

This gives us

`y - 1 = 0`

ANSWER TO QUESTION 3

The equation of a straight line in the slope intercept form is

`y = mx + c`

where m is the slope and c is the y-intercept.

Thus,


`m = - (1)/(3)`
and

`c = (10)/(3)`

We substitute in to the formula to obtain,


`y = - (1)/(3) x + (10)/(3)`

we multiply through by 3 to obtain,


`3y = - x + 10`

We rewrite in general form by equating everything to zero.

Thus,


`3y + x - 10 = 0`

Or


`x + 3y - 10 = 0`

The correct answer is option D.

ANSWER TO QUESTION 4

We want to write the equation of the line that has an x-intercept of -3 and passes through the point (-3, 7).

This implies that the line passes through the points,


`(-3,0) \: and \: (-3,7)`

We find the slope as follows,


`m = (7 - 0)/( - 3 - - 3) = (7 - 0)/( - 3 + 3)`

This implies that,

`m= (7)/(0)`
The slope is undefined. This means the line is parallel to the y-axis.

The equation of a line that has an undefined slope or parallel to the y-axis is given by


`x=x_1`

where

`x_1 = - 3`

Therefore the equation is

`x = - 3`

The correct answer is A.

or you could have also obtained the equation as follows using any of the points.


`y - 7 = (7)/(0) (x + 3)`

This implies that,


`0(y - 7) = 7(x + 3)`


`0 = 7(x + 3)`

We divide through by 7 to get,

`0 = x + 3`

hence

`x = - 3`

Answer 2

In y = mx + b form, the slope is in the m position and the y int is in the b position

1. slope of -4....y int of -3
y = -4x - 3 <==

2. (-2,1)(2,1)...u have the same y coordinates..this means u have a horizontal line with a slope of 0.
y = 1......y - 1 = 0 <===

3. slope = -1/3 and y int = 10/3...
y = -1/3x + 10/3....add 1/3 to both sides
1/3x + y = 10/3...multiply everything by 3
x + 3y = 10
x + 3y - 10 = 0 <==

4. (-3,7)...and if the x int is -3, then its points are (-3,y)...meaning u have points where the x coordinates are the same...meaning vertical lines...ur answer is x = -3