Question

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Answer 1

Please check the explanation.

Explanation:

1)

From the graph, taking the two points

(3, -5)

(-3, 5)

The slope between (3, -5) and (-3, 5) will be:

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`m=(5-\left(-5\right))/(-3-3)`

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

Therefore, the slope is:

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

2)

1ST METHOD

We know that the y-intercept of the graph of the linear function can be determined by setting x=0 and solving for y

• As the graph crosses the y-axis at x=0

From the graph, it is clear that:

at x=0, y=0

Thus, the y-intercept is: (0, 0)

2ND METHOD

We know that the slope-intercept form of the line equation is

`y=mx+b`

where 'm' is the slope and 'b' is the y-intercept

substituting the point (3, -5) and m=-5/3 in the slope-intercept form

`y=mx+b`

`-5=(-5)/(3)\left(3\right)+b`

`(-5)/(3)\left(3\right)+b=-5`

`-5+b=-5`

`b=0`

Thus, the y-intercept is: (0, 0)

3)

We know that the slope-intercept form of the line equation is

`y=mx+b`

substituting m=-5/3 and b=0 to determine the equation line in the slope-intercept form

`y=(-5)/(3)x+0`

Therefore, the equation line in the slope-intercept form is:

`y=(-5)/(3)x+0`

where m=-5/3 and b=0