Читать книгу Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice) - Mary Jane Sterling, Mary Sterling Jane - Страница 11

Chapter 4

Graphs and Equations of Lines

Lines are graphs of linear expressions. When graphing lines or writing their equations, you have the slope intercept form, , or you can use the point-slope form, .Slopes of parallel lines are equal in value, and slopes of perpendicular lines are negative reciprocals of one another.

The Problems You’ll Work On

In this chapter, you’ll work with the graphs and equations of lines in the following ways:

 Graphing a line given a point and a slope

 Graphing lines given two points

 Graphing a line parallel or perpendicular to a particular line

 Writing the equation of a line given a point and a slope

 Writing the equation of a line given two points

 Writing the equations of lines either parallel or perpendicular to a given line

What to Watch Out For

Don’t let common mistakes like those that follow trip you up when working with the graphs and equations of lines:

 Drawing a line with a positive slope rather than a negative slope

 Not using the slope formula correctly when inserting the coordinates of points

 Forgetting to change the sign when determining the slope of a line perpendicular to a given line

 Distributing incorrectly when simplifying the point-slope form

Sketching Lines Using a Point and Slope

191–210 Sketch a graph of the line described.

191. Through (3, 2) with

192. Through (–2, –3) with

193. Through (0, 3) with

194. Through (3, –2) with

195. Through (1, 3) and parallel to the line

196. Through (5, 1) and parallel to the line

197. Through (–2, –3) and parallel to the line

198. Through (–3, –1) and parallel to the line

199. Through (4, 1) and parallel to the line

200. Through (0, 0) and parallel to the line

201. Through (2, 4) and perpendicular to the line

202. Through (–3, –3) and perpendicular to the line

203. Through (–2, 7) and perpendicular to the line

204. Through (4, –1) and perpendicular to the line

205. Through (2, 3) and perpendicular to the line

206. Through (–2, 4) and perpendicular to the line

207. Through (2, 5) and perpendicular to the line

208. Through (1, –1) and perpendicular to the line

209. Through (4, 3) and perpendicular to the x-axis

210. Through (3, –5) and perpendicular to the y-axis

Writing Equations of Lines Given Point and Slope

211–220 Write an equation of the line with the given point and slope.

211. Through (3, –1);

212. Through (3, –1);

213. Through (3, –1);

214. Through (3, –1);

215. Through (3, –1);

216. Through (3, –1);

217. Through (3, –1);

218. Through (3, –1);

219. Through (3, –1);

220. Through (3, –1); m is undefined

Writing Equations of Lines Given Two Points

221–228 Write an equation of the line through the two points.

221. (3, –2) and (4, 2)

222. (–5, 1) and (–3, 7)

223. (4, –3) and (1, 6)

224. (–2, –3) and (3, 4)

225. (5, 6) and (–1, 12)

226. (–3, 5) and (4, –4)

227. (6, 3) and (6, –8)

228. (4, –2) and (5, –2)

Finding Equations of Parallel Lines

229–234 Write an equation of the line parallel to the given line through the point.

229. Parallel to through (1, 1)

230. Parallel to through (2, 3)

231. Parallel to through (3, 0)

232. Parallel to through (0, 5)

233. Parallel to through (4, 8)

234. Parallel to through (4, –7)

Writing Equations of Perpendicular Lines

235–240 Write an equation of the line perpendicular to the given line through the point.

235. Perpendicular to through (2, 3)

236. Perpendicular to through (10, –7)

237. Perpendicular to through (–2, 3)

238. Perpendicular to through (–9, –1)

239. Perpendicular to through (–6, 2)

240. Perpendicular to through (5, –3)