Question 632868
write the equation, in slope intercept form,for each of the following lines:

through (-1,7) and (4,0)


slope=1/2, through (-2,8)


through (6,-2)and parallel to y=7x-1


through (6,-2)and perpendicular to y=7x-1



Thank you soo much for your help. I am attepting to finish these problems but I am failing.


In order to form an equation of a line, one needs to know the slope (m), and at least 1 point


I will do the 1st one, and you should be able to do the rest. I think that's fair enough.


We find the slope, or m, by using the slope formula, {{{(y[2] - y[1])/(x[2] - x[1])}}}


Therefore, for the points, (-1,7) and (4,0), we get the slope, or m = {{{(0 - 7)/(4 - - 1)}}}, or {{{- 7/5}}}


Using the slope, or m of {{{- 7/5}}}, and the coordinate point, (4, 0), we use the point-slope formula, {{{y - y[1] = m(x - x[1])}}} to get: 


{{{y - 0 = (- 7/5)(x - 4)}}} ----- {{{y = (- 7/5)x + (7/5)(4)}}}


{{{highlight_green(y = (- 7/5)x + 28/5))}}}


OR


{{{y = (- 7/5)x + 28/5}}}


5y = - 7x + 28 ------- Multiplying by LCD, 5


{{{highlight_green(7x + 5y = 28)}}}.....(Standard Form of equation of the line)


HINTS:

For number 2, you already have the slope (m), and a point, so you should be able to determine the equation of the line


For number 3, you'll need to find the slope, based on the given equation. The equation of the line that you're trying to find will have the same slope. Along with the slope, and the coordinate point, you can determine the equation of the line. 


For number 4, you'll need to find the slope, based on the given equation. The equation of the line that you're trying to find will have a slope that is the NEGATIVE RECIPROCAL of the slope you just found. Along with the slope, and the coordinate point, you can determine the equation of the line. 


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