Answer:
For figure 1: The equation of a line is y=1
For figure 2: The equation of a line is y=(-4)x+1
For figure 3:The equation of a line is y=![\frac{-5}{2}x+5](https://tex.z-dn.net/?f=%5Cfrac%7B-5%7D%7B2%7Dx%2B5)
Step-by-step explanation:
The equation of line slope-intercept form is given by y=mx+c
Where m is the slope of the line and c is the y-intercept.
For figure 1:
Here, Line is parallel to x-axis
Hence, Slope m=0
Also, Line passing to y axis at (0,1)
Y-intercept is c=1
Therefore,
The equation of line is
y=0x+1
y=1
For figure 2:
Figure show a line passing through point (1,-3) and (-1,5)
The slope of the line is given by m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
Using given points to find out the slope of a line
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{5-(-3)}{(-1)-1}](https://tex.z-dn.net/?f=%5Cfrac%7B5-%28-3%29%7D%7B%28-1%29-1%7D)
m=![\frac{8}{-2}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B-2%7D)
m=(-4)
Also, Line is intersecting y-axis at (0,1)
Hence, c=1
We can write the equation of line as
y=mx+c
y=(-4)x+1
Thus, The correct option is D). y=(-4)x+1
For figure 3:
From the figure, a line is passing through points (-2,0) and (0,5)
The slope of the line is given by m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
Using given points to find out the slope of a line
m=![\frac{Y2-Y1}{X2-X1}](https://tex.z-dn.net/?f=%5Cfrac%7BY2-Y1%7D%7BX2-X1%7D)
m=![\frac{5-0}{0-(-2)}](https://tex.z-dn.net/?f=%5Cfrac%7B5-0%7D%7B0-%28-2%29%7D)
m=![\frac{-5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-5%7D%7B2%7D)
Also, Line is intersecting y-axis at (0,5)
Hence, c=5
We can write the equation of line as
y=mx+c
y=![\frac{-5}{2}x+5](https://tex.z-dn.net/?f=%5Cfrac%7B-5%7D%7B2%7Dx%2B5)