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What is the equation of a line with slope 3/4 and passing through (-1, -6). Write it in slope-intercept form.?

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3 Answers

You should recognize that you have been given a slope and an ordered pair which is a point consisting of an x and y coordinate.  You can use the Point-Slope equation for a linear line very easily by just plugging in these values.  y - (-6) = 3/4(x - (-1).  The next step is you need to solve for y.  Solving for y will put this in the desired slope-intercept form of a linear equation y = mx + b.  Remember you end up working with fractions so make sure you add/subtract after finding a common denominator.  The solution is y = (3/4)x - 21/4.
The equation is going to be of the form y=(3/4)x+something.  It passes through (-1,-6)
In order to walk to the y-axis from (-1,-6) you need to walk 1 step positive in x, from -1 to 0.
In order to stay on the line you must then walk up 3/4 step in y to -5 1/4=-21/4
y=(3/4)x-21/4
 
First we have the point slope formula:
y-y1=m(x-x1)     ................ equation1
 
Here in the given question, y1=-6 ,x1=-1
Plugging these values in equation 1
[y-(-6)]=3/4[x-(-1)]
y+6=3/4(x+1)
y+6=3/4x+3/4
y=3/4x-21/4