TurntechGodhead666
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Write the slope-intercept form of the equation of the line through the given point with the
given slope.
through: (2,-2), slope = -5/6

Sagot :

rvkacademic

Answer:

[tex]\rm y = -\dfrac{5}{6} x-\dfrac{1}{3}[/tex]

Step-by-step explanation:

The slope intercept form of a line equation is

y = mx + b where m is the slope and b the y-intercept

Slope is given as [tex]- \dfrac{5}{6}[/tex]

So equation of line is
[tex]\rm y = -\dfrac{5}{6}x + b\\\\We\;can\;find\;bby\;substituting\;the\;x,\;y\;values\;for\;point\;(2,\;-2)\;into\;the\;equation\\\rm y = -\dfrac{5}{6}x + b\\\\\\\rm We\;can\;find\;by\;substituting\;the\;x,\;y\;values\;for\;point\;(2,\;-2)\;into\;the\;equation\\\\-2 = -\dfrac{5}{6}\times2 + b\\\\-2 = -\dfrac{10}{6} + b\\\\-2 = -\dfrac{5}{3} + b\\\\[/tex]

[tex]\rm Adding\;\dfrac{5}{3} \;to\;both\;sides\;:\\\dfrac{5}{3} - 2 = b\\\\\dfrac{5-6}{3} = b\\\\b = -\dfrac{1}{3}[/tex]

So equation of line is
[tex]\rm y = -\dfrac{5}{6} x-\dfrac{1}{3}[/tex]

darianamin

Answer:

[tex]\huge\boxed{y=-\frac{5}{6}x-\frac{1}{3}}[/tex]

Useful Information:

The equation of a straight line: [tex]y=mx+c[/tex]

Step-by-step explanation:

To work this out you would first need to substitute the gradient into the equation, this gives you[tex]y=-\frac{5}{6}x+c[/tex].

The next step is to substitute the x and y coordinates from the point (2,-2) into the equation, this gives you [tex]-2=-\frac{5}{6}(2)+c[/tex]

In order to work out the value of c, you would have to bring the value of [tex]-\frac{5}{6}(2)[/tex] over to the other side, this can be done by adding [tex]\frac{5}{6}(2)[/tex] or [tex]-\frac{5}{3}[/tex] to -2, which gives you [tex]-\frac{1}{3}[/tex].

The final step is to substitute the m value of  [tex]-\frac{5}{6}[/tex] and the c value of  [tex]-\frac{1}{3}[/tex] into the equation, this gives you [tex]y=-\frac{5}{6}x-\frac{1}{3}[/tex]

1) Substitute the gradient.

[tex]y=-\frac{5}{6}x+c[/tex]

2) Substitute the x and y coordinates.

[tex]-2=-\frac{5}{6}(2)+c[/tex]

3) Bring [tex]-\frac{5}{6}(2)[/tex] over to the other side.

[tex]c=-2+\frac{5}{6}(2)[/tex]

4) Simplify to find the value of c.

[tex]c=-\frac{1}{3}[/tex]

5) Substitute the m and c values.

[tex]y=-\frac{5}{6}x-\frac{1}{3}[/tex]

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