Question

Find the equation of the line through point (8, -9) and perpendicular to 3x +8y =4

Answer 1

Answer:

3y = 8x - 91

y = 8/3 * x - 30 1/3

Step-by-step explanation:

First we can find the slope of the second line.

Let's rewrite the equation as 8y=44-3x.

After dividing both sides of the equation by 8 we'll get an equivalent equation y = 5.5 - 3/8 * x. The coefficient of x is the slope -> the slope is -3/8. In order for the line to be perpendicular to this line the product of the slopes of two lines should be equal to -1 or in other words the slopes have to be opposite reciprocals of each other. The reciprocal of -3/8 is -8/3. Opposite to it is 8/3. Now we know the slop and the coordinates of a point on the line (given). Let's make the equation of the line in the form of y = mx+ b. We can plug in values for m, y and x. m = 8/3(slope), y=-9 (second coordinate of the point), x = 8 (first coordinate). We got

-9 = 8/3 * 8 +b

Now we need to solve the equation to find b

b =-91/3 or -30 1/3

Answer 2

Answer:

Slope = -0.750/2.000 = -0.375

Geometric figure: Straight Line

Slope = -0.750/2.000 = -0.375

x-intercept = 4/3 = 1.33333

y-intercept = 4/8 = 1/2 = 0.50000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3*x+8*y-(4)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve 3x+8y-4 = 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 3x+8y-4 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/2 so this line "cuts" the y axis at y= 0.50000

y-intercept = 4/8 = 1/2 = 0.50000

Calculate the X-Intercept :

When y = 0 the value of x is 4/3 Our line therefore "cuts" the x axis at x= 1.33333

x-intercept = 4/3 = 1.33333

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 0.500 and for x=2.000, the value of y is -0.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.250 - 0.500 = -0.750 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -0.750/2.000 = -0.375

Geometric figure: Straight Line

Slope = -0.750/2.000 = -0.375

x-intercept = 4/3 = 1.33333

y-intercept = 4/8 = 1/2 = 0.50000