SLOPE OF A LINE JOINING TWO GIVEN POINTS WORKSHEET

Find the slope of the line through each pair of points.

Problem 1 :

(8, 10), (-7, 14)

Solution

Problem 2 :

(-3, 1), (-17, 2)

Solution

Problem 3 :

(-20, -4), (-12, -10)

Solution

Problem 4 :

(-12, -5), (0, -8)

Solution

Problem 5 :

(-19, -6) and (15, 16)

Solution

Problem 6 :

(-6, 9) and (7, -9)

Solution

Problem 7 :

(-18, -20) and (-18, -15)

Solution

Problem 8 :

(12, -18) and (11, 12)

Solution

Problem 9 :

The line that passes through the points (3, -7) and (14, k) has the slope of 5/6. Determine the exact value of k.

Solution

Problem 10 :

The triangle on the right has horizontal side AC and vertical side BC. If the line segment AB has slope of 11/5, determine the area of the triangle ABC to the nearest tenth of a square centimeter.

Solution

Problem 11 :

A line with slope 3/7 passes through the point (4, 2). Is the point (-130, -57) on this line? Explain.

Solution

Problem 12 :

The rhombus shown in the diagram on the below has an area of 90 square units. Determine the slope of the line segment AD.

Solution

Find the value of x and y so that the line through the pair of points has the given slope.

Problem 1 :

(x, 3) and (5, 9) and slope (m) = 2

Solution

Problem 2 :

(-2, 3) and (4, y) and slope (m) = -3

Solution

Problem 3 :

(-3, -5) and (4, y) and slope (m) = 3

Solution

Problem 4 :

(-8, -2) and (x, 2) and slope (m) = 1/2

Solution

Problem 5 :

What is an equation of the graph shown?

a) y = −2x − 8     b) y = x - 8       c) y = − x − 8      d) y = 2 x − 8

Solution

Problem 6 :

f(x) = 2x + 3

For the given function f, the graph of y = f(x) in the xy-plane is parallel to line j. What is the slope of line j ?

Solution

Problem 7 :

Line l goes through points P and Q, whose coordinates are (0, 1) and (b, 0), respectively. For which of the following values of b is the slope of line l greater than −1/2 ?

a) 1/2       b)  1       c) 3/2      d)  5/3      e)  5/2

Solution

Problem 8 :

The function h is defined by h(x) = 4x + 28. The graph of y = h(x) in the xy-plane has an x-intercept at (a, 0) and a y-intercept at (0, b), where a and b are constants. What is the value of a + b ?

a) 21       b)  28       c) 32      d)  35

Solution

Problem 9 :

Lien l is defined by 3y + 12x = 5. The line n is perpendicular to the line l in the xy-plane. What is the slope of line n ?

Solution

Convert from the given standard form of a linear equation to the slope-intercept form of a linear equation.

Problem 1 :

x + 5y = 5

Solution

Problem 2 :

3x + 2y = 4

Solution

Problem 3 :

y = (-11x/10) - 1

Solution

Problem 4 :

y = -2x - 9

Solution

Problem 5 :

You have $6 to spend on apples and bananas.

(a) Graph the equation 1.5x + 0.6y = 6, where x is the number of pounds of apples and y is the number of pounds of bananas.

(b) Interpret the intercepts.

Solution

Problem 6 :

Define two variables for the verbal model. Write an equation in slope-intercept form that relates the variables. Graph the equation.

a)  ($2.00/pound) ⋅ Pounds of peaches + ($1.50/pound) ⋅ Pounds of apples = $15

b) (16 miles/hour) ⋅ Hours biked + (2 miles/hour) ⋅ Hours walked = 32 miles

Solution

Problem 7 :

A charm bracelet costs $65, plus $25 for each charm.

a. Write an equation in standard form that represents the total cost of the bracelet.

b. How much does the bracelet shown cost?

Solution

Answer Key

1)  the slope = -1/5 and y-intercept = 1.

2)  slope = -3/2 and y-intercept = 2.

3) the standard form is 11x + 10y + 10 = 0.

4) the standard form is 2x + y + 9 = 0.

5) a) 

b) The x-intercept shows that you can buy 4 pounds of apples if you don’t buy any bananas. The y-intercept shows that you can buy 10 pounds of bananas if you don’t buy any apples.

6) a) 

b)

7) a) y = 65 + 25x

b)  the total cost is $390.