The slope of the line is 2. Why? Well, see below for an explanation!
The slope of a line is found by using the formula rise/run (rise over run). This means that by starting at the initial value of the y-intercept, 3, we would count how many units away we are from the next complete point. We do so by counting from left to right, and in this case, going up and then to the right. To get from the point (0, 3) to the point (1, 5), we would move two spaces vertically along the y-axis and one space horizontally along the x-axis. Because the slope of the line is found using the formula m = rise over run, the slope would be 2/1 because we went up 2 points and to the right one. When simplifying, we will find that 2 divided by 1 equals 2. Hence, our slope is 2.
Your final answer: The slope of the line is 2/1 or 2. If you need extra help, let me know and I will gladly assist you.
Answer:
We have a slope and a point, this way, we do not need to find the slope using two points. We can find the line using the Slope Form to turn it into Slope-Intercept Form, also known as "y = mx + b". We can use the Slope Form which is "y - y1 = m(x - x1)". A coordinate is "(x,y)", so that means, "(-1,4)" means that x = -1 and y = 4. We can substitute y1 for 4 and x1 for -1, and m for -5 since m is the slope. Plugging that information into the Slope Form Formula we get "y - 4 = -5(x - (-1))". We know that a negative with a negative turn positive, so we can use this information to change the formula to "y - 4 = -5(x + 1)". Now we distribute and simplify, these steps are shown below.
y - 4 = -5(x + 1)
y - 4 = -5x -5
y - 4 + 4 = -5x - 5 + 4
y = -5x - 1
Now that we have simplified it, we can see that the slope is -5 and the -1 is the y-intercept. To check this is a linear equation is to graph it, or substitute three x-coordinate or y-coordinates and draw a line. In conclusion, the equations is y = -5x - 1.
Step-by-step explanation:
Step-by-step explanation:
4x² - 12x + 9 = 5 → 4x² - 12x + 4 = 0 → x² - 3x + 1 = 0
∆ = b² - 4ac → ∆ = (-3)² -4(1)(1) = 9 - 4 = 5
x = (-(-3) ± √5)/2(1) = (3 ± √5)/2
x² - 3x + 1 = 0 → (x - 3/2)² - 9/4 + 1 = 0 → (x - 3/2)² = 5/4 → x - 3/2 = ±√5 / 2 → x = ½( 3 ± √5)
Option A is correct.
Step-by-step explanation:
We need ti identify the radius of circle.
The radius of circle is a length of the line from center of the circle to anywhere on the edge of circle. It is also shown in the figure attached.
From the given options, only FE is the line that goes from center of circle to the edge of circle. So, FE is the radius of the circle.
So, Option A is correct.
Keyword: Radius of circle
Learn more about Radius of circle at:
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Answer:
The constant of proportionality is 
Step-by-step explanation:
The constant of proportionality is the ratio between two directly proportional quantities
- If x and y are in directly proportion, then
, where k is the constant of proportionality.
- The direct proportion can be represented by a line whose equation is y = kx, where k is the slope of the line.
<em>To find the constant of proportionality from the given graph choose a point on the line and substitute x and y in the equation of the proportionality by the coordinates of the point.</em>
∵ Point (4, 18) lies on the line
∴ x = 4, y = 18
∵ The equation is y = kx
→ Substitute x by 4 and y by 18
∴ 18 = k(4)
∴ 18 = 4k
→ Divide both sides by 4 to find k
∴ 
∴ 
→ Simplify the fraction by dividing up and down by 2
∴ 
∴ The constant of proportionality is
