The main contents of this chapter include all of the following: Inverse circular functions, derivatives of inverse circular functions, integrals yielding the inverse circular functions. | General Mathematics ADE 101 Unit 2 LECTURE No. 14 TYPES OF LINEAR EQUATIONS Today’s Objectives Knowledge Test Point – Slope Form To write an equation of a line in point – slope form, all you need is Any Point On The Line The Slope (x1, y1) m Once you have these two things, you can write the equation as y – y1 = m (x – x1) That’s “y minus the y-value of the point equals the slope times the quantity of x minus the x-value of the point”. Example Write the equation of the line that goes through the point (2, –3) and has a slope of 4. Point = (2, –3) Slope = 4 y – y1 = m (x – x1) y + 3 = 4 (x – 2) Starting with the point – slope form Plug in the y-value, the slope, and the x-value to get Notice, that when you subtracted the “–3” it became “+3”. y – y1 = m (x – x1) Starting with the point – slope form Plug in the y-value, the slope, and the x-value to get Notice, that when you subtracted the “–4” it became “+4”. Write the equation of the line that goes through the point (–4, 6) and has a slope of . Point = (–4, 6) Slope = y – 6 = (x + 4) Example Write the equation of the line that goes through the points (6, –4) and (2, 8) . Point = (6, –4) Slope = –3 y + 4 = –3 (x – 6) We have two points, but we’re missing the slope. Using the formula for slope, we can find the slope to be Point = (2, 8) Slope = –3 To use point – slope form, we need a point and a slope. Since we have two points, just pick one IT DOESN’T MATTER BOTH answers are acceptable more on why later. y – 8 = –3 (x – 2) Using the first point, we have, Using the second point, we have, y2 – y1 x2 – x1 Example Slope-intercept Form An equation whose graph is a straight line is a linear equation. Since a function rule is an equation, a function can also be linear. m = slope b = y-intercept Y = mx + b (if you know the slope and where the line crosses the y-axis, use this form) Writing Equations in Slope – Intercept Form y + 4 = –3 (x – 6) y – 8 = –3 (x – 2) Earlier we wrote an equation of the line that . | General Mathematics ADE 101 Unit 2 LECTURE No. 14 TYPES OF LINEAR EQUATIONS Today’s Objectives Knowledge Test Point – Slope Form To write an equation of a line in point – slope form, all you need is Any Point On The Line The Slope (x1, y1) m Once you have these two things, you can write the equation as y – y1 = m (x – x1) That’s “y minus the y-value of the point equals the slope times the quantity of x minus the x-value of the point”. Example Write the equation of the line that goes through the point (2, –3) and has a slope of 4. Point = (2, –3) Slope = 4 y – y1 = m (x – x1) y + 3 = 4 (x – 2) Starting with the point – slope form Plug in the y-value, the slope, and the x-value to get Notice, that when you subtracted the “–3” it became “+3”. y – y1 = m (x – x1) Starting with the point – slope form Plug in the y-value, the slope, and the x-value to get Notice, that when you subtracted the “–4” it became “+4”. Write the equation of the line that goes through the point (–4, 6) .
