A. The equation of the line is y = -0.2 x + 1.9
B. The equation of the line is y = 4 x + 3
C. The equation of the line is y = -8
D. The equation of the line is y = 2 x + 4
Step-by-step explanation:
The slope-intercept form of the equation of a line is y = m x + b, where
m is the slope of the line and b is the y-intercept
A.
∵ The line passes through points (2 , 1.5) and (-5 , 36.5)
∴ [tex]x_{1}[/tex] = 2 and [tex]x_{2}[/tex] = -5
∴ [tex]y_{1}[/tex] = 1.5 and [tex]y_{2}[/tex] = 36.5
∵ [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∴ [tex]m=\frac{-5-2}{36.5-1.5}=\frac{-7}{35}=\frac{-1}{5}[/tex]
∴ m = -0.2
∵ y = m x + b
∵ m = -0.2
∴ y = -0.2 x + b
- To find b substitute x and y in the equation by the coordinates of
 one of the two given points
∵ x = 2 and y = 1.5
∴ 1.5 = -0.2(2) + b
∴ 1.5 = - 0.4 + b
- Add 0.4 to both sides
∴ 1.9 = b
∴ y = -0.2 x + 1.9
The equation of the line is  y = -0.2 x + 1.9
B.
∵ m = 4
∵ y = m x + b
∴ y = 4 x + b
∵ Point (3 , 15) lies on the line
- To find b substitute x and y in the equation by the coordinates
 of the given point
∵ x = 3 and y = 15
∴ 15 = 4(3) + b
∴ 15 = 12 + b
- Subtract 12 from both sides
∴ 3 = b
∴ y = 4 x + 3
The equation of the line is y = 4 x + 3
C.
∵ The line has the same slope of line y = 1
- The line whose equation y = 1 is a horizontal line
∵ The slope of the line y = 1 is zero because it is a horizontal line
∴ m = zero
∵ y = m x + b
∴ The equation of the line is y = (0)x + b
∴ y = b
∵ The line passes through point (3 , -8)
- In the horizontal line the y-coordinates of all point lie on the line
 are equal
∴ The line intersect the y-axis at point (0 , -8)
∴ b = -8
∴ y = -8
The equation of the line is y = -8
D.
∵ m = 2
∵ y-intercept is at point (0 , 4)
∴ b = 4
∵ y = m x + b
∴ y = 2 x + 4
The equation of the line is y = 2 x + 4
Learn more:
You can learn more about the linear equations in brainly.com/question/4326955
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