Sara is trying to find an equation for a line that passes through (5, 2) and is perpendicular to 3x + 2y = 15. Explain the steps
that Sara could take to determine the equation. A) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the slope of that line and the point (5, 2) into the point-slope formula. B) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. C) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. D) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (0, 0) into the point-slope formula.
1 answer:
Not on your list, but an easy way is
.. a) swap coefficients of x and y, negating one. (Now you have 2x -3y.)
.. b) set any constant term to zero (now you have 2x -3y = 0)
.. c) translate the line to the point (5, 2) by substituting x ⇒ x-5, y⇒ y-2
2(x -5) -3(y -2) = 0
The way you've been taught, selection C is the proper choice.
.. a) swap coefficients of x and y, negating one. (Now you have 2x -3y.)
.. b) set any constant term to zero (now you have 2x -3y = 0)
.. c) translate the line to the point (5, 2) by substituting x ⇒ x-5, y⇒ y-2
2(x -5) -3(y -2) = 0
The way you've been taught, selection C is the proper choice.
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The graph of linear equation 2x - 3y = -12 is as shown below.
I this question, we have been given a linear equation 2x - 3y = -12
We need to graph the points.
For x = 1,
2(1) - 3y = -12
2 - 3y = -12
-3y = -14
y = 14/3
For x = 0,
2(0) - 3y = -12
y = (-12)/(-3)
y = 4
For x = -1,
2(-1) - 3y = -12
-3y = -12 + 2
y = (-10) / (-3)
y = 10/3
So, we get coordinates (1, 14/3), (0, 4) and (-1, 10/3)
Now we plot these points.
The graph of linear equation 2x - 3y = -12 is as shown below.
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