Question

Help help I don’t really get this???

Answer 1

Question 4:
`y=\displaystyle -(4)/(5)x`

Question 5:
`y=-5x-3`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope of the line and b is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).

Question 4

1) Determine the slope (m)

`\displaystyle m=(y_2-y_1)/(x_2-x_1)` where two points that pass through the line are
`(x_1,y_1)` and
`(x_2,y_2)`

In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:

`\displaystyle m=(-4-4)/(5-(-5))\\\\\displaystyle m=(-4-4)/(5+5)\\\\\displaystyle m=(-8)/(10)\\\\\displaystyle m=-(4)/(5)`

Therefore, the slope of the line is
`\displaystyle -(4)/(5)`. Plug this into
`y=mx+b` as the slope (m):

`y=\displaystyle -(4)/(5)x+b`

2) Determine the y-intercept (b)

On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (b) is 0. Plug this into
`y=\displaystyle -(4)/(5)x+b`:

`y=\displaystyle -(4)/(5)x+0\\\\y=\displaystyle -(4)/(5)x`

Question 5

1) Determine the slope (m)

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:

`\displaystyle m=(-3-2)/(0-(-1))\\\\\displaystyle m=(-3-2)/(0+1)\\\\\displaystyle m=(-5)/(1)\\\\m=-5`

Therefore, the slope is -5. Plug this into
`y=mx+b`:

`y=-5x+b`

2) Determine the y-intercept (b)

On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (b) is -3. Plug this into
`y=-5x+b`:

`y=-5x+(-3)\\y=-5x-3`

I hope this helps!