Question

1. Find the slope between (-1, -3) and (4, 0)

a. 5/3
b. -3
c. - 3/5
d. 3/5
2. Given the equation: 3y = 15x + 9, find slope.
a. 5
b. 2/3
d. -2/3
c. Undefined
3. Given a point and a slope, write the equation in slope-intercept form; (1, 2) and m= -3
a. y = -3x + 1
b. y = -3x – 5
c. y = -3x + 5
d. y = -3x – 1
4. Write the equation of the line in slope-intercept form: y-int = (0,3) , m = 2
a. y = 2x + 3
b. y = -2x + 3
c. y = 2x
d. y = 3x +2
5. Given two points, write the equation in point-slope form: (1, 3) and (-2, 12)
a. y – 1 = -3(x – 3)
b. y – 3 = 5(x – 1)
c. y – 3 = -3(x – 1)
d. y + 12 = -3(x – 1)
6. Write the equation of the function graphed below.
a. y= x - 1
b. y= -x - 4
c. y = x - 4
d. y = x +1
7. The table below represents a linear function. What is the slope of this function?
a. 1/3
b. -1/3
c. 3
d. -3

Answer 1

Explanation:

1. Slope = (y2-y1) / (x2-x1) = -3-0/ -1-4= -3/-5= 3/5 (d)

2.

Compare to the equation y= mx+b, where m is the slope

3y = 15x+9 divide by 3 each term

y = 15x/3 +9/3

y= 5x + 3 so slope is 5 ( a)

3.

use first the equation point- slope y-y1 =m (x-x1) and rearange it to be in slope-intercept form y=mx +b

y-y1 =m (x-x1)

y-2 = -3( x-1)

y = 2-3x+3

y= -3x +5 ( c)

4.

if the point y- intercept is at (0, 3) then the y-intercept is b=3

y= mx+b

y = 2x +3 (a)

5.

the equation point- slope y-y1 =m (x-x1), find the slope m= (y2-y1) / (x2-x1)

m= 3-12/ 1+2 = -9/3 = -3

y-1 = -3(x-3) is (a)

6.

y-intercept is at -4 ( yet the graph is off a bit -tell your teacher)

slope m = 1

so the equation is y=mx+b and here is y=x -4 (c)

7.

the slope is m= (y2-y1) / (x2-x1) si pich any two points from the table and calculate the slope

for example (0, 3) and (1, 0)

m = (3-0)/ (0-1) = 3/-1 = -3 (d)

Answer 2

1. The slope between (-1, -3) and (4, 0) is: d. 3/5.

2. The slope of the equation 3y = 15x + 9 is: a. 5.

3. The equation in slope-intercept form is: c. y = -3x + 5.

4. The equation of the line in slope-intercept form is: a. y = 2x + 3.

5. The equation in point-slope form is: c. y – 3 = -3(x – 1).

6. The equation of the function graphed above is: c. y = x - 4.

7. The slope of this function is: d. -3

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Slope(m) = (0 + 3)/(4 + 1)

Slope(m) = 3/5.

Part 2.

The slope-intercept form of the equation of a straight line refers to the general equation of a linear function and it is represented by this mathematical equation;

y = mx + b

Where:

• m is the slope.
• x and y are the points.
• b is the y-intercept.

By rewriting the equation 3y = 15x + 9 in slope-intercept form, we have;

y = 5x + 19/3

slope (m) = 5.

Part 3.

At data point (1, 2) and a slope of -3, an equation for this line can be calculated by using the point-slope form as follows:

`y - y_1 = m(x - x_1)`

y - 2 = -3(x - 1)

y = -3x + 5

Part 4.

At data point (0, 3) and a slope of 2, an equation for this line can be calculated by using the point-slope form as follows:

`y - y_1 = m(x - x_1)`

y - 3 = 2(x - 0)

y = 2x + 3

Part 5.

Slope (m) = (12 - 3)/(-2 - 1)

Slope (m) = -3.

At data point (1, 3) and a slope of -3, an equation for this line can be calculated by using the point-slope form as follows:

y - 3 = -3(x - 1).

Part 6.

With an x-intercept (a) of (4, 0) and a y-intercept (b) of (0, -4), an equation for the graph is given by;

x/a + y/b = 1

x/4 - y/4 = 1

x - y = 4

y = x - 4

Part 7.

Based on the table of vaues, the slope is as follows;

Slope(m) = (0 - 3)/(1 - 0)

Slope(m) = -3.