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Question: How do you find the slope and y-intercept of \(y=-9x\)?...

How do you find the slope and y-intercept of y=−9xy=-9x?

Explanation

Solution

We will use the help of graphs to solve this question. We will first plot the graph of the above equation and then to find the slope of the given equation, we will two point of the line of the graph and put it in the formula for slope, we will find y-intercept by putting the value of x=0x=0, and we get the y-intercept as 0 and the point is origin (0,0)(0,0).

Complete step by step solution:
According to the question we are provided with an equation whose slope and y-intercept is to be found.
If we take a closer look at the equation, it will correspond to a linear graph which extends in the 2nd and the 4th quadrant.
We will start plotting by finding the coordinates for the given equation, we have,

  1. When x=0x=0,
    Then,y=−9xy=-9x
    Substituting the value of x, we get
    y=−9(0)=0y=-9(0)=0
    The coordinate is (0,0)(0,0).

  2. When x=1x=1
    Substituting the value of x, we get
    y=−9(1)=−9y=-9(1)=-9
    The coordinate is (1,−9)(1,-9).

  3. When x=−1x=-1
    Substituting the value of x, we get
    y=−9(−1)=9y=-9(-1)=9
    The coordinate is (−1,9)(-1,9).

  4. When x=2x=2
    Substituting the value of x, we get
    y=−9(2)=−18y=-9(2)=-18
    The coordinate is (2,−18)(2,-18).

  5. When x=−2x=-2
    Substituting the value of x, we get
    y=−9(−2)=18y=-9(-2)=18
    The coordinate is (−2,18)(-2,18).
    The graph with the above coordinates are as below,

    To find the slope we will take two points, let say, (2,−18)(2,-18) and (1,−9)(1,-9)
    We will substitute these in the formula for slope which is:
    slope=y2−y1x2−x1slope=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}
    Let,
    (2,−18)=(x1,y1)(2,-18)=({{x}_{1}},{{y}_{1}}) and (1,−9)=(x2,y2)(1,-9)=({{x}_{2}},{{y}_{2}})
    Substituting we get,
    ⇒slope=−9−(−18)1−2\Rightarrow slope=\dfrac{-9-(-18)}{1-2}
    ⇒slope=−9+181−2\Rightarrow slope=\dfrac{-9+18}{1-2}
    ⇒slope=9−1\Rightarrow slope=\dfrac{9}{-1}
    ⇒slope=−9\Rightarrow slope=-9
    Now, to find the y-intercept, we will put x=0x=0, we get,
    y=−9xy=-9x
    Substituting the value of x, we get
    y=−9(0)=0y=-9(0)=0
    The point is origin (0,0)(0,0).
    Therefore, the slope of the given equation is -9 and the y-intercept is 0.

Note: To find the slope of the given equation, we can also compare it with the equation of a line which is y=mx+cy=mx+c, where m is the slope and c is the constant and is the y-intercept.
On comparing the given equation, that is, y=-9x
we get,
slope, m=−9m=-9 and y-intercept, c=0c=0.