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3 years ago

Find the slope of a line that is perpendicular to the line 4x + 3y - 15 = 0.

1 answer:

4 0

<h2>3x-4y-15=0 </h2><h2>Geometric figure: Straight Line</h2><h2> Slope = 1.500/2.000 = 0.750</h2><h2> x-intercept = 15/3 = 5</h2><h2> y-intercept = 15/-4 = -3.75000</h2><h2>Step by step solution :</h2><h2>Step 1 :</h2><h2>Equation of a Straight Line</h2><h2> 1.1 Solve 3x-4y-15 = 0 </h2><h2 /><h2>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). </h2><h2 /><h2>"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.</h2><h2 /><h2>In this formula :</h2><h2>y tells us how far up the line goes</h2><h2>x tells us how far along</h2><h2>m is the Slope or Gradient i.e. how steep the line is</h2><h2>b is the Y-intercept i.e. where the line crosses the Y axis</h2><h2>The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-4y-15 = 0 and calculate its properties</h2><h2>Calculate the Y-Intercept :</h2><h2>Notice that when x = 0 the value of y is 15/-4 so this line "cuts" the y axis at y=-3.75000</h2><h2> y-intercept = 15/-4 = -3.75000 </h2><h2>Calculate the X-Intercept :</h2><h2>When y = 0 the value of x is 5/1 Our line therefore "cuts" the x axis at x= 5.00000</h2><h2> x-intercept = 15/3 = 5 </h2><h2>Calculate the Slope :</h2><h2>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 -3.750 and for x=2.000, the value of y is -2.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.250 - (-3.750) = 1.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)</h2><h2> Slope = 1.500/2.000 = 0.750 </h2><h2>Geometric figure: Straight Line</h2><h2> Slope = 1.500/2.000 = 0.750</h2><h2> x-intercept = 15/3 = 5</h2><h2> y-intercept = 15/-4 = -3.75000</h2><h2>Hope This Helps!!!</h2>

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Answer:

<em>The area of the triangle DEF is 10.</em>

Step-by-step explanation:

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A triangle of base B and height H (both must be perpendicular) has an area of:

$\displaystyle A=\frac{BH}{2}$

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

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With these two values, we calculate the area:

$\displaystyle A=\frac{5*4}{2}=10$

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