The equation for line p can be written as y = -1/2x + 8. Line q, which is perpendicular to line p, includes the point (4,7). 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. ______

Perpendicular Lines Slopes: Line q is perpendicular to line p. Are their slopes the same or opposite reciprocals? Slopes of perpendicular lines are opposite reciprocals.Equation of Line p: Equation of line p: y = -1/2x + 8 Find the slope of line p. Compare y = -1/2x + 8 with y = mx + b. m = -1/2 Slope of line p: -1/2Slope of Line q: Line q is perpendicular to p. Slope of line p: -1/2 Find the slope of line q. Opposite reciprocal of -1/2 is 2. Slope of line q: 2Finding Y-Intercept: For line q: Slope (m): 2 Point: (4, 7) Plug these values in y = mx + b and find the y-intercept. 7 = 2(4) + b 7 = 8 + b 7 - 8 = b -1 = bEquation of Line q: For line q: Slope (m): 2 y-intercept (b): -1 What is the equation of the line q in slope-intercept form? Substitute 2 for m and -1 for b in y = mx + b. y = 2x - 1

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The equation for line $p$ can be written as $y = -\frac{1}{2}x + 8$ . Line $q$ , which is perpendicular to line $p$ , includes the point $(4,7)$ . What is the equation of line $q$ ? $\newline$ Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Math Problems

Algebra 1

Write an equation for a parallel or perpendicular line

Full solution

Q. The equation for line

p

can be written as

y = -\frac{1}{2}x + 8

. Line

q

, which is perpendicular to line

p

, includes the point

(4,7)

. What is the equation of line

q

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Perpendicular Lines Slopes: Line $q$ is perpendicular to line $p$ . Are their slopes the same or opposite reciprocals? $\newline$ Slopes of perpendicular lines are opposite reciprocals.
Equation of Line p: Equation of line p: $y = -\frac{1}{2}x + 8$ $\newline$ Find the slope of line p. $\newline$ Compare $y = -\frac{1}{2}x + 8$ with $y = mx + b$ . $\newline$ $m = -\frac{1}{2}$ $\newline$ Slope of line p: $-\frac{1}{2}$
Slope of Line q: Line q is perpendicular to p. $\newline$ Slope of line p: $-\frac{1}{2}$ $\newline$ Find the slope of line q. $\newline$ Opposite reciprocal of $-\frac{1}{2}$ is $2$ . $\newline$ Slope of line q: $2$
Finding Y-Intercept: For line $q$ : $\newline$ Slope ( $m$ ): $2$ $\newline$ Point: $(4, 7)$ $\newline$ Plug these values in $y = mx + b$ and find the y-intercept. $\newline$ $7 = 2(4) + b$ $\newline$ $7 = 8 + b$ $\newline$ $7 - 8 = b$ $\newline$ $-1 = b$
Equation of Line q: For line q: $\newline$ Slope $m$ : $2$ $\newline$ y-intercept $b$ : $-1$ $\newline$ What is the equation of the line q in slope-intercept form? $\newline$ Substitute $2$ for $m$ and $-1$ for $b$ in $y = mx + b$ . $\newline$ $y = 2x - 1$