Unit 5: Day 5

Today, Students will be able to write and equation out of a line given data points.

The standard form of a linear equation is:

y = mx + b

Where m = slope and b = y-intercept.

2

Calculate the slope of the line. The slope can be found by selecting two points on the line, determining the vertical rise and the horizontal run between the points and dividing them. For example, if (3,4) and (5,6) are on the line, the slope between them would be (5 - 3) / (6 - 4), simplified to (2) / (2), simplified to 1. Include negative values, since slopes can be positive or negative.

3

Determine or calculate the y-intercept of the line. The y-intercept is the y-coordinate of the point where the line passes through the y-axis of the coordinate plane. For example, if the point of intersection with the y-axis is (0,5), the y-intercept would be 5. The y-intercept can be found by physically locating it on the graph or by locating the given point on the line that has an x-coordinate of 0. That point is the point of intersection. The y-intercept will be positive if it intersects the y-axis above the x-axis or negative if it intersects below the x-axis.

4

Write the equation y = mx + b, substituting the values for m and b you calculated or determined. The m will be your slope, and the b will be your y-intercept. Leave the y and x variables in the equation as letter variables. Include the sign of the numbers you plug in. For example, if I discovered my slope to be -3 and my y-intercept to be 5, my linear equation would be y = -3x + 5. The linear equation is complete and correctly written when the (m) and (b) are properly incorporated into the equation.

Quiz

1) Write an equation of the line with a slope of 3 and a y-intercept of 7.
2)Write an equation of the given points.    (4, 2) (0, 3)
3)a. Write an equation of the line that is parallel to the line y 4x 8 
and passes through the point (0, 2).
b. Write an equation of the line that is perpendicular to the line 
y 5x 1 and passes through the point (0, 9).

Answers

1) y =mx +b Write general slope-intercept equation.

y=3x +( 7) Substitute 3 for m and 7 for b.

y =3x+ 7 Simplify.

2) A.Find the slope m using the labeled points.

m

2-3/4-0 =-1/4= -1/-4

B. Find the y-intercept b. The line crosses 

the y-axis at (0, 3), so b 3.

C. Write an equation of the form y mx b.

y=-1/-4x+3

3)a. The slope of the given line is 4, so the slope of the parallel line is

also 4. The parallel line passes through (0, 2), so its y-intercept is 2.

Answer An equation of the line is y =4x+2.

b. Because the slope of the given line is 5, the slope of the 

perpendicular line is the negative reciprocal of 5, or -1/-5

. The 

perpendicular line passes through (0, 9), so its y-intercept is 9.

Answer An equation of the line is y=1/5 x+(- 9), or y=1/5x-9

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