I am a little confused on my homework.

Question

Write the equation in slope-intercept form. Then graph the equation. 

1. 4x+5y=15 
2. x-y+4=0 
3. 5(x+3+y)=10x 
4. 2x+3y-4=x+5

Answer 1

(1).

Graph the linear equation by using slope-intercept method :

The equation 4x+5y=15.

Write the above equation in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

Substract both sides with 4x

5y = 15 - 4x

Divide both sides with 5

y = (15 - 4x)/5

y = 3 - 4/5x

y = -4/5x +3

Slope : m = -4/5 and y-intercept : b = 3.

y-intercept is 3, so the line crosses the y-axis at (0, 3)

Using slope find the next point.

Slope = rise/run = -4/5

Start at point (0, 3), move 4 units down (3-4=-1) and 5 units right (0+5=5), then plot the point (5,-1).

Draw a line through these points.

Graph :

Answer 2

(3).

Graph the linear equation by using slope-intercept method :

The equation 5(x+3+y)=10x.

Write the above equation in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

Divide both side with 5

x+3+y = 2x

Substract both sides with x+3

y = x - 3

Slope : m = 1 and y-intercept : b = -3.

y-intercept is -3, so the line crosses the y-axis at (0, -3)

Using slope find the next point.

Slope = rise/run = 1

Start at point (0, -3), move 1 unit up (-3+1=-2) and 1 units right (0+1=1), then plot the point (1,-2).

Draw a line through these points.

Graph :

Answer 3

(4).

Graph the linear equation by using slope-intercept method :

The equation 2x+3y-4=x+5.

Write the above equation in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

Substract both sides with 2x-4

2x+3y-4 -2x +4 =x+5-2x +4

3y=-x+9

Divide both sides with 3

y= -1/3x +3

Slope : m = -1/3 and y-intercept : b = 3.

y-intercept is 3, so the line crosses the y-axis at (0, 3)

Using slope find the next point.

Slope = rise/run = -1/3

Start at point (0, 3), move 1 unit down (3-1=2) and 3 units right (0+3=3), then plot the point (3,2).

Draw a line through these points.

Graph :

Answer 4

(2).

Graph the linear equation by using slope-intercept method :

The equation x-y+4=0.

Write the above equation in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

Add both side with y

x-y+4+y = y

y = x + 4

Slope : m = 1 and y-intercept : b = 4.

y-intercept is 4, so the line crosses the y-axis at (0, 4)

Using slope find the next point.

Slope = rise/run = 1

Start at point (0, 4), move 1 unit up (4+1=5) and 1 units right (0+1=1), then plot the point (1,5).

Draw a line through these points.

Graph :