A student expanded an expression, as shown. Is the student's work correct? Explain why or why not.
2 answers:
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<u>Answer: </u>
Equation of a line that is perpendicular to y = 3x-4 and that passes through the point (2 -3) is
<u>Solution: </u>
The slope - intercept form equation of line is given as
y = mx+c ----- (1)
Where m is the slope of the line. The coefficient of “x” is the value of slope of the line.
Given that
3x -y = 4
Converting above equation in slope intercept form,
y = 3x - 4 ---- (2)
On comparing equation (1) and (2) we get slope of equation (2) is m=3
Consider equation of the line which is perpendicular to equation (2) is --- eqn 3
If two lines having slope m1 and m1 are perpendicular then relation between their slope is
That is if slope of the line (2) is 3 then slope of equation (3) is
On substituting value of m1 in equation (3), we get
--- eqn 4
Given that equation (4) passes through (2, -3) that is x = 2 and y = -3. So on substituting value of x and y in equation (4),
On simplifying above equation,
On substituting value of b in equation (4),
Hence equation of a line that is perpendicular to y=3x-4 and that passes through the point (2 -3) is