4 Slope/Standard Form questions...?

Question

1. Find the x and y intercepts of the line given the equation: 7x+2y=-21

2. Write the equation 2y=12-5x in standard form.

3. What is the standard form of the equation y=1/4x-3?

4. Find the slope and y-intercept of the line: 5x-3y=19

Answer 1

The equation is 7x + 2y = -21 - (1)

The x-intercept a  and y-intercept b then the equation form  is x / a + y / b = 1

We change the equation intercept form then

Divide each side by  -21 for the equation - (1)

Therefore 7x / -21 + 2y / -21 = -21 / -21

Simplify

x  / -3 + y / (-21 / 2) = 1

This equation is a standard form

Therefore x-intercept a = -3 and y-intercept b = -21 / 2.

Answer 2

The equation is 2y = 12 - 5x

The equation of the standard form is y = mx + c here m is slope and c is y-intercept

Divide each side by 2

2y / 2 = (12 - 5x) / 2

Simplify

y = 6 - (5 /2)x

Therefore y = -(5 /2)x + 6

m = -5 / 2 and c = 6

The equation of the standard form is y = -(5 / 2)x + 6.

Comments

Standard form of the line 2y = 12 - 5x is 5x + 2y = 12.

Answer 3

The equation is y = (1 / 4)x - 3

The standard form of the equation is ax + by = c here a,b and c are integers

Multiply each side by 4 to the equation

4y = [(1 / 4)x - 3]4

4y = (1 / 4)4x -3(4)

Simplify

4y = x - 12

subtract 4y from each side

4y - 4y = x - 12 - 4y

0 = x - 4y -12

Add 12 to each side

Therefore x -4y = 12

The equation of the standard form is x + (-4)y = 12.

Answer 4

The equation is 5x - 3y = 19

The slope intercept form is y = mx + c here m is a slope and c is y-intercept

we change the equation in to slope intercept form

Add 3y to each side

5x - 3y + 3y = 19 + 3y

5x = 3y + 19

subtract 19 from each side

5x-19 = 3y + 19 - 19

Simplify

There fore 3y = 5x - 19

Divide each side by 3

3y / 3 = (5x - 19) / 3

y = (5 / 3)x + (-19 / 3)

This form is a slope intercept form

Therefore slope m = 5 /3 and y-intercept c = -19 / 3.

 

Answer 5

1.
7x+2y=-21
write the equation in slope-intercept form y =mx + b. m = slope and b is y-intercept.
y = -7/2x -21/2
y-intercepts is -21/2.
x-intercept is where the line crosses the x-axis, so y = 0
x-intercept = -21/7=-3
2.
Standard form line equation is Ax + By = C
2y=12-5x
add 5x to each side
5x+2y = 12
3.
Standard form line equation is Ax + By = C
y=1/4x-3
multiply each side by 4
4y = x-12
standard form line equations is
x-4y = 12
4.
Write the equation in slope-intercept form y =mx + b. m = slope and b is y-intercept.
5x-3y=19
y = 5/3x -19/3
slope = 5/3 and y-intercept = -19/3