Question

(1st pic) What is the equation of the line shown in this graph?

(2nd pic) What is the equation of this line in slope-intercept form?
a. y=4x−1
b. y = 4x + 1
c. y= -1/4x+1
d. y= -4x+1
(3rd pic) What is the equation of the line in slope-intercept form? y=_ x + _

Answer 1

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=
`(-5)/(2)x+5`

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=
`(Y2-Y1)/(X2-X1)`

Using given points to find out the slope of a line

m=
`(Y2-Y1)/(X2-X1)`

m=
`(5-(-3))/((-1)-1)`

m=
`(8)/(-2)`

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=
`(Y2-Y1)/(X2-X1)`

Using given points to find out the slope of a line

m=
`(Y2-Y1)/(X2-X1)`

m=
`(5-0)/(0-(-2))`

m=
`(-5)/(2)`

Also, Line is intersecting y-axis at (0,5)

Hence, c=5

We can write the equation of line as

y=mx+c

y=
`(-5)/(2)x+5`