Algebra HELP PLEASE!!!!!!!?

Question

7) Write an equation of the line that passes through (2,3) and (4, 7).
A) y = 2x - 1
B) y = 2x + 15
C) y = -2x - 1
D) y = -2x + 15
8) Find an equation of the line that has intercepts (1,0) and (0,4).
A) y = 4x - 1
B) y = -4x + 4
C) y = -4x + 1
D) y = -4x - 4
9) 3x + 8y - 36 = 0
The point (x, 3/4) is a solution to the equation shown. What is the value of x?
A) -14
B) -10
C) 0
D) 10
10) Write an equation of the line that is parallel to y = 1/2x + 3 and passes through the point (10, -5).
A) y = 2x - 15
B) y = -2x + 15
C) y = - 1/2 x
D) y = 1/2 x - 10
11) A line passes through the point (5, -2) and has a slope of -1/3 Which equation models the line?
A)y - 2 = -1/3 (x - 5)
B) y + 2 = -1/3 (x - 5)
C) y - 5 = -1/3 (x - 2)
D) y - 5 = -1/3 (x + 2)
12) Suppose an airplane climbs 15 feet for every 40 feet it moves forward. What is the slope of this airplane's ascent?
13) A HORIZONTAL line passes through point (-3, -1). Find the equation of this line.
A) x = 1
B) x = 3
C) y = -1
D) y = -3x + 3
14) 3x + 4y = 7
7x + 2y = 12
.Maria has two linear equations and wants to determine if their graphs are parallel. Which strategy could be used to solve the problem?
A) Plug in 0 for y to determine the x-intercepts.
B) Plug in 0 for x to determine the y-intercepts.
C) Write the equations in slope-intercept form and compare the slopes.
D) Write the equations in slope-intercept form and compare the y-intercept

Answer 1

7)

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Let the points are (x₁, y₁) = (2, 3) and (x₂, y₂) = (4, 7).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(7 - 3)/(4 - 2)]

m  = [4/2]

⇒ m = 2.

Now, the line equation is y = 2x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (2, 3).

3 = (2)(2) + b

b = 3 - 4

⇒ b = -1.

The line equation in slope - intercept - form is y = 2x - 1

Option A is correct .

Answer 2

8) The intercepts are (1, 0) (0, 4)

x intercpt is 1 and y intercept is 4.

The equation of a line with x, y intercepts is x/a + y/b = 1

Where a is x intercept and b is y intercept.

a = 1 and b = 4

So the line is x/1 + y/4 = 1

(4x + y)/4 = 1

4x + y = 4

y = - 4x + 4

Option B is correct.

Answer 3

9) The equation 3x + 8y - 36 = 0

(x, 3/4) is solution

Substitute for (x, y) = (x, 3/4) in equation

3x + 8(3/4) - 36 = 0

3x + 6 - 36 = 0

3x - 30 = 0

3x = 30

x = 10

Option d is correct.

Answer 4

11)

Equation of a line in point - slope form is y - y₁ = m (x - x₁)

Substitute for (x₁, y₁) = (5, - 2)  and m = -1/3 in above equation.

y - (- 2) = - 1/3(x - 5)

y + 2 = - 1/3(x - 5)

Option B is correct.

Answer 5

12)

 The airplane climbs 15 feet for every 40 feet it move forward.

So the first order pair is (15, 40)

And the next order pair is (30, 80)

(x₁, y₁) = (15, 40) and (x₂, y₂) = (30, 80)

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

= (80 - 40)/(30 - 15)

= 40/15

= 8/3

Slope of the airplane ascent = 8/3.

Answer 6

13) A horizontal line passes through (- 3, - 1)

Slope of the horizontal line is zero.

Horizontal line equation is y = b

Where b is the y coordinate .

Substitute for b = - 1

y = - 1

Option c is correct.

Answer 7

14) To determine the two linear equations are parallel.

Step 1 : write the equations in slope intercept form(y = mx + b) and compare the slopes.

Step 2 : if the two linear equations have equal slopes then they are parallel.

Option c is correct.