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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.

Use the graph of the line to find the xintercept yintercept and slope Write the slopeintercept form of the equation of the line class=

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SaniShahbaz

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:

[tex]slope=m=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}[/tex]

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:

[tex]m=\frac{-9-0}{0-(-9)}=-1[/tex]

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:

[tex]y=mx+c[/tex]

where,

m = slope of line = -1

c = y-intercept = -9

Using these values, the equation becomes:

[tex]y=-x- 9[/tex]

Answer:

x-intercept: [tex]-9[/tex].

y-intercept: [tex]-9[/tex].

Slope: [tex]-1[/tex]

Equation: [tex]y=-x-9[/tex]

Step-by-step 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 [tex](-9,0)[/tex], therefore, x-intercept is [tex]-9[/tex].

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 [tex](0,-9)[/tex], therefore, y-intercept is [tex]-9[/tex].

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

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-9-0}{0-(-9)}=\frac{-9}{0+9}=\frac{-9}{9}=-1[/tex]

Therefore, the slope of the line is [tex]-1[/tex].

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

[tex]y=mx+b[/tex], where,

m = Slope,

b = The y-intercept.

[tex]y=-1(x-(-9))[/tex]

[tex]y=-1(x+9)[/tex]

[tex]y=-x-9[/tex]

Therefore, the equation of the line would be [tex]y=-x-9[/tex].

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