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Find the equation of a line containing the given point and the slope.   (-3/4, 7) and...

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Find the equation of a line containing the given point and the slope. 

 (-3/4, 7) and m = -3. 

Leave improper fractions improper.

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embizze's profile pic

Posted (Answer #1)

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Given a point `(x_1,y_1)` and a slope m the equation of theline is `y-y_1=m(x-x_1)`

So the equation is `y-7=-3(x-(-3/4))`

`y-7=-3(x+3/4)` in point-slope form.

We can solve for y to get the equation in slope-intercept form:

`y=-3x-9/4+7`

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`y=-3x+19/4` in slope-intercept form.

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Then we can put into standard form:

`4y=-12x+19`

`12x+4y=19` in standard form.

Wiggin42's profile pic

Posted (Answer #2)

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 (-3/4, 7) and m = -3. 

Point-slope is the easiest method when given a slope and a point: 

y - y1 = m(x - x1) where m is slope and (x1, y1) is a point. 

Plug in: 

y - 7 = -3(x + (3/4)

You can distribute the -3 and solve for y to get slope-intercept form. 

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