What is the equation of a line that has a slope of 4/5 and passes through the point (-2,4)?
1 answer:
Answer:
y = x + 5
Step-by-step explanation:
Let's do it in slope-intercept form, it will look like this:
m = slope
b = y -intercept
To find our equation we will plug in the slope, plug in the point given, and solve for b.
y = mx + b
y = x + b
4 = (-2) + b
4 = + b
5 = b
Plug the b into our original equation, and there is our answer!
y = x + 5
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Answer: < -4/5, 3/5>
This is equivalent to writing < -0.8, 0.6 >
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Explanation:
Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.
We have a right triangle with legs of 4 and 3. The hypotenuse is through use of the pythagorean theorem.
We have a 3-4-5 right triangle.
Therefore, the vector is 5 units long. This is the magnitude of the vector.
Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.
Therefore, we go from < -4, 3 > to < -4/5, 3/5 >
This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6
Side note: Unit vectors are useful in computer graphics.
