{"id":92,"date":"2022-04-13T09:57:35","date_gmt":"2022-04-13T09:57:35","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=92"},"modified":"2025-03-05T07:27:06","modified_gmt":"2025-03-05T07:27:06","slug":"d-19-write-an-equation-for-a-parallel-or-perpendicular-line","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/d-19-write-an-equation-for-a-parallel-or-perpendicular-line\/","title":{"rendered":"D.19 Write an equation for a parallel or perpendicular line"},"content":{"rendered":"\n

Write an equation for a parallel or perpendicular line<\/strong><\/h2>\n\n\n\n

key notes:<\/p>\n\n\n\n

Perpendicularlineshaveslopesthatareoppositereciprocals, like a\/b and -b\/a. opposite reciprocals have a product of -1.<\/h3>\n\n\n\n

The slope-intercept form<\/strong> of a linear equation is<\/p>\n\n\n\n

y=mx+b<\/p>\n\n\n\n

where m<\/em> is the slope and b<\/em> is the y<\/em>-intercept.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

Line s has an equation of y = 3x + 4. Parallel to line s is line t, which passes
through the point (1, 6). <\/p>\n\n\n\n

What is the equation of line t?<\/p>\n<\/div><\/div>\n\n\n\n

Step 1: Find the slope of line s.<\/p>\n\n\n\n

First, find the slope m of line s. This is the only time you will use the equation of line s.<\/p>\n\n\n\n

y = mx + b<\/p>\n\n\n\n

y = \u20133x + 4<\/p>\n\n\n\n

Line s has a slope m of 3.
Step 2: Find the slope of line t.<\/strong>
Line t is parallel to s, so its slope is the same: -3.
Step 3: Use the slope of line t and a point on line t to find its
y-intercept.<\/strong>
Plug the slope m = 3 and the point (1, 6) into the slope-intercept formula.
Then solve for the y-intercept b.
y = mx + b
6 = 3(1) + b Plugin y = 6, m = 3, and x = 1
6 = 3 + b Multiply
9 = b Add 3 to both sides
Line t has a y-intercept of 9.
Step 4: Use the slope of line t and the y-intercept of line t to find the
equation of the line.
Plug the slope m =- 3 and the y-intercept b = 9 into the slope-intercept
formula.
y = mx + b
y = 3x + 9 Plugin m = -3 and b = 9
The equation of line t in slope-intercept form is y = -3x + 9<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Line k has an equation of y = 2x + 7. Line l, which is perpendicular to line k,
includes the point (2, 7). <\/p>\n\n\n\n

What is the equation of line l?<\/p>\n<\/div><\/div>\n\n\n\n

Step 1: Find the slope of line k.
First, find the slope m of line k. This is the only time you will use the equation of line k.
y = mx + b
y = 2x + 7
Line k has a slope m of -2.<\/p>\n\n\n\n

Step 2: Find the slope of line l.
Line l is perpendicular to k, so its slope is the opposite reciprocal: 1\/2.
Step 3: Use the slope of line l and a point on line l to find its y-intercept.<\/p>\n\n\n\n

Step 3: Use the slope of line l and a point on line l to find its y-intercept.<\/p>\n\n\n\n

Plug the slope m=1\/2 and the point(2, \u20137) into the slope-intercept formula. Then solve for they-intercept b.<\/p>\n\n\n\n

y = mx + b<\/p>\n\n\n\n

\u20137 =1\/2 ( 2 )+b Plugin y= \u20137,m=1\/2, and x= 2<\/p>\n\n\n\n

\u20137 = 1 + b Multiply and simplify<\/p>\n\n\n\n

\u20138 = b Subtract1 from both sides<\/p>\n\n\n\n

Line l has ay-intercept of\u20138.<\/p>\n\n\n\n

Step 4: Use the slope of line l and the y-intercept of line l to find the equation of the line.<\/p>\n\n\n\n

Plug the slope m=1\/2 and they-intercept b = \u20138 in to the slope-intercept formula.<\/p>\n\n\n\n

y = mx + b<\/p>\n\n\n\n

y =1\/2 x+\u20138 Plugin m=1\/2 and b= \u20138<\/p>\n\n\n\n

y =1\/2 x\u2212 8
Rewrite as subtraction<\/p>\n\n\n\n

The equation of line in slope-intercept form is y=1\/2 x\u2212 8<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

The equation of line g is y =1\/7x \u2212 8. Line h includes the point (9, 1) and is parallel to line g. <\/p>\n\n\n\n

What is the equation of line h?<\/p>\n<\/div><\/div>\n\n\n\n

Step 1: Find the slope of line g.
First find the slope m of line g. This is the only time you will use the equation of
line g.
y = mx + b
y =1\/7x \u2212 8
Line g has a slope m of 1\/7.<\/p>\n\n\n\n

Step 2: Find the slope of line h.
Line h is parallel to g, so its slope is the same:1\/7.
<\/p>\n\n\n\n

Step 3: Use the slope of line h and a point on line h to find its
y-intercept. Plug the slope m =1\/7 and the point (9, 1) into the slope-intercept formula.
Then solve for the y-intercept b.
y = mx + b
1 =1\/7(9) + b Plug in y = 1, m =1\/7, and x = 9
1 =9\/7+b Multiply = b Subtract 9\/7 from both sides = b Rewrite with a common denominator
= b Subtract Line h has a y-intercept of -2\/7.
Step 4: Use the slope of line h and the y-intercept of line h to find the
equation of the line.
Plug the slope m =1\/7and the y-intercept b =-2\/7 into the slope-intercept
formula.
y = mx + b
y =1\/7x +-2\/7 Plug in m =1\/7 and b =-2\/7
y =1\/7x \u22122\/7 Rewrite as subtraction<\/p>\n\n\n\n


.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n
\"\"<\/figure>\n<\/div>\n\n\n\n
\n