Line p has an equation of y = –8x + 6. Line q, which is perpendicular to line p, includes the point (2,–2). What is the equation of line q? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers. ______

Question

Line p has an equation of y = –8x + 6. Line q, which is perpendicular to line p, includes the point (2,–2). What is the equation of line q? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.   ______

Bytelearn · Accepted Answer

Find Slope of Line p: Line p has a slope of -8, as we can see from its equation y = -8x + 6. Since line q is perpendicular to line p, we need to find the slope of line q, which will be the negative reciprocal of the slope of line p.Determine Slope of Line q: The negative reciprocal of -8 is 1/8. Therefore, the slope of line q is 1/8.Calculate Y-Intercept of Line q: Now we need to find the y-intercept of line q. We know that line q passes through the point (2, -2) and has a slope of 1/8. We can use the point-slope form of the equation of a line to find the y-intercept. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.Apply Point-Slope Form: Plugging in the slope and the point (2, -2) into the point-slope form, we get y - (-2) = 1/8(x - 2). Simplifying this, we get y + 2 = 1/8x - 1/4.Isolate y in Equation: To get the equation in slope-intercept form, we need to isolate y. Subtracting 2 from both sides of the equation, we get y = 1/8x - 1/4 - 2.Simplify Final Equation: Simplifying the equation further, we combine the constant terms -1/4 and -2. Since -2 is the same as -8/4, we get y = 1/8x - 1/4 - 8/4, which simplifies to y = 1/8x - 9/4.

Line $p$ has an equation of $y = -8x + 6$ . Line $q$ , which is perpendicular to line $p$ , includes the point $(2, -2)$ . What is the equation of line $q$ $?$ $\newline$ Write the equation in slope-intercept form.

Full solution

More problems from Write an equation for a parallel or perpendicular line

Related topics

Line p p p has an equation of y=−8x+6 y = -8x + 6 y=−8x+6. Line q q q, which is perpendicular to line p p p, includes the point (2,−2) (2, -2) (2,−2). What is the equation of line q q q???\newlineWrite the equation in slope-intercept form.

Line $p$ has an equation of $y = -8x + 6$ . Line $q$ , which is perpendicular to line $p$ , includes the point $(2, -2)$ . What is the equation of line $q$ $?$ $\newline$ Write the equation in slope-intercept form.