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Sagot :
ANSWERS
(a) 6/5
(b) y - 16 = 6/5(x - 8)
(c) y = 6/5x + 32/5
EXPLANATION
(a) The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]In this case, we know that the line passes through points (8, 16) and (-2, 4), so its slope is,
[tex]m=\frac{16-4}{8-(-2)}=\frac{12}{8+2}=\frac{12}{10}=\frac{6}{5}[/tex]Hence, the slope of the line is 6/5.
(b) The equation of a line in point-slope form is,
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x₁, y₁) is a point on the line. Here, we know two points where the line passes through, so we can use either to write the equation. Using the point (8, 16),
[tex]y-16=\frac{6}{5}(x-8)[/tex]Hence, the equation of the line in point-slope form is y - 16 = 6/5(x - 8).
(c) The equation of a line in slope-intercept form is,
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
To rewrite the equation we found in part (b) in slope-intercept form, first, apply the distributive property to the slope on the right side of the equation,
[tex]\begin{gathered} y-16=\frac{6}{5}x-\frac{6}{5}\cdot8 \\ \\ y-16=\frac{6}{5}x-\frac{48}{5} \end{gathered}[/tex]And then, add 16 to both sides,
[tex]\begin{gathered} y-16+16=\frac{6}{5}x-\frac{48}{5}+16 \\ \\ y=\frac{6}{5}x+\frac{32}{5} \end{gathered}[/tex]Hence, the equation in slope-intercept form is y = 6/5x + 32/5.
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