To determine the point-slope equation, we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points and m is the slope.
First, let's calculate the slope:
m = (y2 - y1)/(x2 - x1)
= (62 - 34)/(10 - 3)
= 28/7
= 4
Now we can choose any of the given points (x1, y1) to plug into the equation. Let's use (3, 34):
y - 34 = 4(x - 3)
Therefore, the point-slope equation for the given data is:
y - 34 = 4(x - 3)
Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain. Given the two points we know: (3, 34) and (10, 62), what would the point-slope equation looK like
9 answers
2x + b = c solve
To solve the equation 2x + b = c, we'll need more information. In order to solve for x and find the values of b and c, we'll need additional equations or numerical values for at least two of the variables.
Triangles ABC and DEF are called similar triangles. b. The slope of the line AG can be written as ΔxΔy c. This is a proportional relationship.
b. The slope of the line AG can be written as Δy/Δx.
c. If the triangles ABC and DEF are similar, then there is a proportional relationship between their corresponding sides. This means that if we denote the lengths of the sides of triangle ABC as AB, AC, and BC, and the lengths of the sides of triangle DEF as DE, DF, and EF, then the ratios of the corresponding side lengths are equal:
AB/DE = AC/DF = BC/EF.
Similarly, if we denote the lengths of the heights (perpendicular distances from one side to the opposite vertex) of triangle ABC as hA, hB, and hC, and the heights of triangle DEF as hD, hE, and hF, then the ratios of the corresponding height lengths are also equal:
hA/hD = hB/hE = hC/hF.
c. If the triangles ABC and DEF are similar, then there is a proportional relationship between their corresponding sides. This means that if we denote the lengths of the sides of triangle ABC as AB, AC, and BC, and the lengths of the sides of triangle DEF as DE, DF, and EF, then the ratios of the corresponding side lengths are equal:
AB/DE = AC/DF = BC/EF.
Similarly, if we denote the lengths of the heights (perpendicular distances from one side to the opposite vertex) of triangle ABC as hA, hB, and hC, and the heights of triangle DEF as hD, hE, and hF, then the ratios of the corresponding height lengths are also equal:
hA/hD = hB/hE = hC/hF.
Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?(1 point) Responses (y−10)=−5(x+10) open paren y minus 10 closed paren is equal to negative 5 times open paren x plus 10 close paren (y−45)=−5(x−3) open paren y minus 45 close paren is equal to negative 5 times open paren x minus 3 close paren (y+10)=−5(x−10) open paren y plus 10 close paren is equal to negative 5 times open paren x minus 10 close paren (y−3)=−5(x−45)
The correct point slope equation for the given data would be:
(y - 10) = -5(x - 10)
(y - 10) = -5(x - 10)
. Using the graph, describe the key characteristics of the graph (positive/negative slope, proportional/non proportional, y-intercept). b. Write in words what the slope of the graph means in context. c. Write in words what the y-intercept of the graph means in context. d. Write in words what the graph of the line is showing.
a. The graph of the equation (y - 10) = -5(x - 10) has a negative slope.
b. The slope of the graph represents the rate of change of the water level of the river. In this case, since the slope is -5, it means that for every 1 unit increase in the number of days without rain (x-axis), the water level decreases by 5 units (y-axis).
c. The y-intercept of the graph represents the initial value of the water level when there are 0 days without rain. In this case, the y-intercept is at (0, 10), implying that even with no days without rain, the water level is still 10 feet.
d. The graph of the line represents the relationship between the number of days without rain and the corresponding water level of the river. As the number of days without rain increases, the water level decreases at a constant rate.
b. The slope of the graph represents the rate of change of the water level of the river. In this case, since the slope is -5, it means that for every 1 unit increase in the number of days without rain (x-axis), the water level decreases by 5 units (y-axis).
c. The y-intercept of the graph represents the initial value of the water level when there are 0 days without rain. In this case, the y-intercept is at (0, 10), implying that even with no days without rain, the water level is still 10 feet.
d. The graph of the line represents the relationship between the number of days without rain and the corresponding water level of the river. As the number of days without rain increases, the water level decreases at a constant rate.