Question

Here are 5 lines on a coordinate grid:
Write equations for lines:

Answer 1

For line a; the equation of the line is x = - 4

For line b, the equation of the line is x = 4.

For line c, the equation of the line is y = 4.

For line d, the equation of the line is y = - 2.

For line e, the equation of the line is y = 3x/4 + 1.

How to write the equation of the line?

The equation of the given line is written by applying the following formula as shown below;

The general equation of line is;

y = mx + c

where;

• m is the slope of the line
• c is the y - intercept of the line

For line a; the line cut across only x - axis at x = - 4,

x = - 4

For line b, the line cut across only x - axis at x = 4,

x = 4

For line c, the line cut across only y axis at y = 4,

y = 4

For line d, the line cut across only y axis at y = -2,

y = - 2

For line e, the slope of the line is calculated by applying the following formula as follows;

m = Δ y / Δ x

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

m = (1 + 2) / 4

m = 3/4

The y - intercept of the line = 1

The equation of the line becomes;

y = 3x/4 + 1

Answer 2

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

For the particular case of horizontal lines, those will be of the form:

y = constant.

The vertical lines will be of the form:

x = constant.

Let's start with line a, this is a vertical line, then will be:

x = constant.

To see the value of the constant, you need to see in which point it intersects the x-axis, in this case is in -4, then line a will be:

x = -4

For line b we have the same reasoning, in this case the line intersects the x-axis at x = 4, then line b is: x = 4.

Now for the horizontal lines:

Line c will be of the form:

y = constant

To find the value of the constant you need to see in which point the line intersects the y-axis.

In this case the line intersects the axis at y = 4.

Then this line can be written as: y = 4

For line d, we can see that it intersects the y-axis at -2, then this line will be written as:

y = -2.

For the case of line e we can use the first thing we wrote, let's find two points that belong to this line.

(0 , 1) and (4, -2)

Then the slope will be:

a = (-2 - 1)/(4 - 0) = -3/4

y = -(3/4)*x + b

To find the value of b, we can just replace the values of one of the points in the equation. I will use the point (0, 1), this means that we must replace x by 0, and y by 1.

1 = -(3/4)*0 + b

1 = b

Then the equation for line e is:

y = -(3/4)*x + 1.