Graph the linear equation.

Question

y = 5

Answer 1

To graph the linear equation y = 5, we need to plot all the points that have a y-coordinate of 5.

The graph will be a horizontal line passing through the point (0, 5). This is because the equation y = 5 means that the y-coordinate of any point on the line will always be 5, regardless of the x-coordinate.

The graph is shown below as a horizontal line passing through the point (0, 5):

y | .
| .
5 | .
| .
--------------------------------
x = 0 x

Answer 2

Graph the linear equation.

y = 1

Answer 3

To graph the linear equation y = 1, we need to plot all the points that have a y-coordinate of 1.

The graph will be a horizontal line passing through the point (0, 1). This is because the equation y = 1 means that the y-coordinate of any point on the line will always be 1, regardless of the x-coordinate.

The graph is shown below as a horizontal line passing through the point (0, 1):

y | .
| .
1 |______[•]
|
--------------------------------
x = 0 x

Answer 4

Write the equation in standard form using integers.

y = - 2/5 x - 4

Answer 5

To write the equation y = -2/5x - 4 in standard form using integers, we need to eliminate the fraction and rearrange the terms.

Multiplying every term by 5 to eliminate the fraction:

5y = -2x - 20

Rearranging the terms in standard form:

2x + 5y = -20

Answer 6

Write the equation in standard form using integers.
y = - 2/5 x -4

Answer 7

To write the equation y = -2/5x - 4 in standard form using integers, we need to eliminate the fraction and rearrange the terms.

Multiplying every term by 5 to eliminate the fraction:

5y = -2x - 20

Rearranging the terms in standard form to write the equation with integer coefficients:

2x + 5y = -20

Answer 8

Write the equation in standard form using integers.

y + 1 = 2/5 (x + 7)

Answer 9

To write the equation y + 1 = 2/5 (x + 7) in standard form using integers, we need to distribute the fraction and rearrange the terms.

First, distribute 2/5 to both terms in the parentheses:

y + 1 = 2/5 * x + 14/5

Next, we can simplify the equation by converting the fraction into an integer term:

Multiply both sides of the equation by 5 to eliminate the fraction:

5(y + 1) = 2x + 14

Expanding the left side of the equation:

5y + 5 = 2x + 14

Rearranging the terms in standard form to write the equation with integer coefficients:

2x - 5y = -9

Answer 10

Find the​ x- and​ y-intercepts of the line that passes through the given points.

(-5, -5), (7, -1)

Answer 11

To find the x-intercept, we need to determine the x-coordinate of the point where the line crosses the x-axis (y = 0).

Using the point-slope formula, we can calculate the slope of the line:
m = (y2 - y1) / (x2 - x1)
m = (-1 - (-5)) / (7 - (-5))
m = -1 + 5 / 7 + 5
m = 4 / 12
m = 1/3

Using the point-slope formula, we can write the equation of the line:
y - y1 = m (x - x1)
y - (-5) = 1/3 (x - (-5))
y + 5 = 1/3 (x + 5)
3y + 15 = x + 5
3y = x - 10
y = (1/3)x - 10/3

To find the x-intercept, substitute y = 0 into the equation:
0 = (1/3)x - 10/3
(1/3)x = 10/3
x = 10

The x-intercept is x = 10.

To find the y-intercept, substitute x = 0 into the equation:
y = (1/3)(0) - 10/3
y = 0 - 10/3
y = -10/3

The y-intercept is y = -10/3.