The line passing through (-2,5) and (2,p) has a gradient of -1/2.

Fnd the value of p

Given:

The line passing through (-2,5) and (2,p) has a gradient of [tex]-\dfrac{1}{2}[/tex].

To find:

The value of p.

Solution:

If a line passes through two points, then the slope of the line is:

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

The line passing through (-2,5) and (2,p). So, the slope of the line is:

[tex]m=\dfrac{p-5}{2-(-2)}[/tex]

[tex]m=\dfrac{p-5}{2+2}[/tex]

[tex]m=\dfrac{p-5}{4}[/tex]

It is given that the gradient or slope of the line is [tex]-\dfrac{1}{2}[/tex].

[tex]\dfrac{p-5}{4}=-\dfrac{1}{2}[/tex]

On cross multiplication, we get

[tex]2(p-5)=-4(1)[/tex]

[tex]2p-10=-4[/tex]

[tex]2p=-4+10[/tex]

[tex]2p=6[/tex]

Divide both sides by 2.

[tex]p=3[/tex]

Therefore, the value of p is 3.

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