Question

What is the slope of the line given by the equation below?

y-20=5(x-2)

a) 20
b) -20
c) 5
d) -2

Answer 1

The slope of the equation y - 20 = 5 (x-2) is 5 .

Option (c) is correct .

Explanation:

As the general form of the equation of a line is given by

y = mx + c

Where m is slope , c is the y - intercept .

As given the expression in the question be as follow .

y - 20 = 5 × (x-2)

Simplify the above

y - 20 = 5x - 10

y = 5x - 10 + 20

y = 5x + 10

Compare this with the equation y = mx + c .

Thus

m = 5

Therefore the slope of the equation y - 20 = 5 (x-2) is 5 .

Option (c) is correct .

Answer 2

Step by step solution : Step 1 :Equation at the end of step 1 : (y - 20) - 5 • (x - 2) = 0 Step 2 :Equation at the end of step 2 : y - 5x - 10 = 0 Step 3 :Equation of a Straight Line 3.1 Solve y-5x-10 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-5x-10 = 0 and calculate its propertiesGraph of a Straight Line : Calculate the Y-Intercept :Notice that when x = 0 the value of y is 10/1 so this line "cuts" the y axis at y=10.00000 y-intercept = 10/1 = 10.00000 Calculate the X-Intercept :When y = 0 the value of x is 2/-1 Our line therefore "cuts" the x axis at x=-2.00000 x-intercept = 10/-5 = 2/-1 = -2.00000 Calculate the Slope :Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 10.000 and for x=2.000, the value of y is 20.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 20.000 - 10.000 = 10.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN) Slope = 10.000/2.000 = 5.000 Geometric figure: Straight Line Slope = 10.000/2.000 = 5.000 x-intercept = 10/-5 = 2/-1 = -2.00000 y-intercept = 10/1 = 10.00000