1. Write an equation in point-slope form for the line through the given point with the given slope.
(-10,-6);m=-5/8
A. y-6=-5/8(x-10)
B. y-6=-5/8(x+10)
C. y+6=-5/8(x+10)
D. y+10=-5/8(x+6)
2. The table below shows the height of a plant as it grows. Which equation in point-slope form gives the plant height at any time?
Time//Height
2 16
4 32
6 48
8 64
A. y-16=8(x-2)
B. y-16=8x-2
C. y+16=8(x+2)
D. The relationship is non linear.
3. Write y=-0.4+0.3 in standard form using integers.
A. 4x+10y=3
B. 4x+10y=-3
C. 4x-10y=3
D. -4x+10y=3
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1:c
2:c
1. To write an equation in point-slope form, which is y - y₁ = m(x - x₁), we need the slope (m) and a point (x₁, y₁) on the line. In this case, the given slope is -5/8 and the given point is (-10, -6). Plugging these values into the point-slope form gives:
y - (-6) = -5/8(x - (-10))
y + 6 = -5/8(x + 10)
So the correct answer is A. y-6=-5/8(x-10).
2. To find the equation for the plant height at any time, we can use the given data points and the point-slope form. Choose any two points from the table, (2, 16) and (4, 32), and use them to calculate the slope (m):
m = (change in y) / (change in x)
= (32 - 16) / (4 - 2)
= 16 / 2
= 8
Now we have the slope (m) and can choose any point from the table as the point (x₁, y₁). Let's choose (2, 16). Plugging the values into the point-slope form gives:
y - 16 = 8(x - 2)
So the correct answer is A. y-16=8(x-2).
3. The equation given, y = -0.4 + 0.3, is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. However, we need to convert it to standard form (Ax + By = C) using integers.
Multiply the equation by 10 to get rid of the decimal:
10y = -4x + 3
Rearrange the equation to put it in the standard form:
4x + 10y = 3
So the correct answer is A. 4x + 10y = 3.