Question

Use the graph of the line to find the​ x-intercept, y-intercept, and slope. Write the​ slope-intercept form of the equation of the line.

Answer 1

x-intercept:
`-9`.

y-intercept:
`-9`.

Slope:
`-1`

Equation:
`y=-x-9`

Explanation:

We have been given a graph of a line on coordinate plane. We are asked to find the x-intercept, y-intercept, and slope.

We know that x-intercept of a function is a point, where graph crosses x-axis.

Upon looking at our given graph, we can see that graph crosses x-axis at point
`(-9,0)`, therefore, x-intercept is
`-9`.

We know that y-intercept of a function is a point, where graph crosses y-axis.

Upon looking at our given graph, we can see that graph crosses y-axis at point
`(0,-9)`, therefore, y-intercept is
`-9`.

We have two points on the line. Let us find slope of line using points
`(-9,0)` and
`(0,-9)`.

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

`m=(-9-0)/(0-(-9))=(-9)/(0+9)=(-9)/(9)=-1`

Therefore, the slope of the line is
`-1`.

Now, we will substitute
`m=-1` and y-intercept
`-9` in slope form intercept of equation as:

`y=mx+b`, where,

m = Slope,

b = The y-intercept.

`y=-1(x-(-9))`

`y=-1(x+9)`

`y=-x-9`

Therefore, the equation of the line would be
`y=-x-9`.

Answer 2

1) x-intercept:

x-intercept is the point where the graph of the equation crosses the x-axis. From the given figure, we can see that the line is crossing the x-axis at -10. Thus the x-intercept is -9

2) y-intercept:

y-intercept is the point where the graph of the equation crosses the y-axis. From the given figure, we can see that the line is crossing the y-axis at -10. Thus the y-intercept is -9

3) Slope:

Slope of a line is calculated as:

`slope=m=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}`

For calculating the slope we can use both intercepts. x-intercept is ordered pair will be (-9, 0) and y-intercept will be (0, -9). So the slope of the line will be:

`m=(-9-0)/(0-(-9))=-1`

Therefore, the slope of the line is -1.

4) Slope intercept form of the line:

The slope intercept form of the line is represented as:

`y=mx+c`

where,

m = slope of line = -1

c = y-intercept = -9

Using these values, the equation becomes:

`y=-x- 9`