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Given the point and slope, write the equation of the line. (-8,6); slope = 1/4

Sagot :

Answer:

[tex]y=\frac{1}{4}x+8[/tex]

Explanation:

Given the properties of a line.

• Point, (x1, y1) = (-8, 6)

,

• Slope, m = 1/4

It is required that we find the equation of the line.

Since we are given a point on the line and its slope, to find the equation of the line, we make use of the slope-point formula for a line.

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the given values.

[tex]\begin{gathered} y-6=\frac{1}{4}\lbrack x-(-8)\rbrack \\ y-6=\frac{1}{4}\lbrack x+8\rbrack \\ \text{Add 6 to both sides} \\ y-6+6=\frac{1}{4}\lbrack x+8\rbrack+6 \\ y=\frac{1}{4}\lbrack x+8\rbrack+6 \\ \text{Open the bracket} \\ y=\frac{1}{4}x+\frac{1}{4}(8)+6 \\ y=\frac{1}{4}x+2+6 \\ y=\frac{1}{4}x+8 \end{gathered}[/tex]

The equation of the line is:

[tex]y=\frac{1}{4}x+8[/tex]

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