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Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5

Use Graph To Find The Slope And Yintercept Of The Line Compare The Values To The Equation Y X5 class=

Sagot :

As given by the question

There are given that the graph of the line.

Now,

To find the slope and y-intercept of the line, first select two intersect point from the graph.

Then,

The points are:

[tex](0,\text{ 5) and (5, 0)}[/tex]

Then,

First find the slope,

So,

From the formula of slope,

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

Where,

[tex]x_1=0,y_1=5,x_2=5,y_2=0[/tex]

Then,

Put all the value into the given formula.

So,

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-\frac{5}{5} \\ m=-1 \end{gathered}[/tex]

Now,

From the standard form of the line,

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

Then,

Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept

So,

[tex]\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}[/tex]

Hence, the value of the y-intercept is 5.

Now,

The line equation is shown below:

[tex]\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}[/tex]

Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.

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