Respuesta :
Solving the given equation for y results in y = (-4/7) x + (a constant).
The new line has a slope that is the negative reciprocal of -4/7. That slope is +7/4.
The new line passes thru (-4, -7). Thus,
the equation for this new line is y - (-7) = (7/4)(x - [-7]), or
y + 7 = (7/4)(x+7)
Let's put this into slope-intercept form:
y = -7 + (7/4)x + (49/4), or y = (7/4)x + (49/4) - 7, or
y = (7/4)x + 21/4 (answer in slope-intercept form)
The new line has a slope that is the negative reciprocal of -4/7. That slope is +7/4.
The new line passes thru (-4, -7). Thus,
the equation for this new line is y - (-7) = (7/4)(x - [-7]), or
y + 7 = (7/4)(x+7)
Let's put this into slope-intercept form:
y = -7 + (7/4)x + (49/4), or y = (7/4)x + (49/4) - 7, or
y = (7/4)x + 21/4 (answer in slope-intercept form)
Answer:
[tex]y=\frac{7}{4} x[/tex]
Step-by-step explanation:
we have the original line equation
[tex]7y + 4x = 3[/tex]
clearing for y:
[tex]7y=-4x+3\\y=\frac{-4}{7}x+ \frac{3}{7}[/tex]
Now we have an equation of the form slope- intercept:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
thus, the slope of the original line is:
[tex]m=\frac{-4}{7}[/tex]
Now to find the new line, since it has to be perpendicular their slopes must satisfy the following:
[tex]m*m_{1}=-1[/tex]
where m is the slope of the original line, and m1 is the slope of the new line:
[tex]\frac{-4}{7}*m_{1}=-1\\ m_{1}=\frac{-1*7}{-4}\\ m_{1}=\frac{7}{4}[/tex]
this is the slope of the new perpendicular line that passes trough the point (-4,-7), so now we use the point slope equation to find the equation of said line:
[tex]y-y_{1}=m_{1}(x-x_{1})[/tex]
where we know [tex]m_{1}=\frac{7}{4}[/tex], and from the point (-4,-7) [tex]x_{1}=-4, y_{1}=-7[/tex]
so we have:
[tex]y-(-7)=\frac{7}{4} (x-(-4))\\y+7=\frac{7}{4} (x+4)[/tex]
and we clear for y to leave the equation in the slope intercept form:
[tex]y=\frac{7}{4} (x+4)-7\\y=\frac{7}{4} x+\frac{7}{4}*4 -7\\\\y=\frac{7}{4} x+7-7\\y=\frac{7}{4} x[/tex]
