Jeremy C.
asked • 01/09/22Find the equation of the line using the point-slope formula. Write the final equation using slope-intercept form. Perpendicular to 5y=x-4 and passes through the point (-2,2)
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1 Expert Answer
Raymond B. answered • 01/09/22
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5y = x-4
divide both sides by 5
y = x/5 -4/5
y = (1/5)x -4/5
the slope is the coefficient of the x term, when the equation is solved for y
slope = 1/5
the perpendicular line has slope = the negative inverse of 1/5, which is -5/1 = -5
the perpendicular line equation is y =-5x + b
plug in the point (-2,2) to solve for b
2 =-5(-2) + b
2 = 10 + b
b = 2-10 = -8
b = -8
y = -5x - 8 is the equation of the perpendicular line through the given point
y = -5x - 8 is in slope intercept form with -5 = slope and -8 = the y intercept
"using the point slope formula" means
(y-2)/(x+2) = slope = -5
y-2 = -5(x+2) = -5x -10
y = -5x -10 + 2
y = -5x - 8
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Colleen S.
Hi Jeremy! First we need to find the slope of the line 5y = x - 4. Put it into slope-intercept form by dividing both sides by 5. We get y = 1/5 x - 4/5. We can then read the slope from this line: 1/5. Since we want to write an equation of a line that is perpendicular to this, we take the opposite reciprocal to get the new slope. The opposite reciprocal of 1/5 is -5/1, or -5. We then move on to writing the new equation. We need it to have slope -5 and pass through (-2, 2). Using point-slope form, we get y - 2 = -5 (x - (-2)). We start solving for y, and get y - 2 = -5 (x + 2), then y - 2 = -5x - 10, then y = -5x - 8. This equation is in slope-intercept form and is the final answer.01/09/22