Graphing lines

Question

Graph the following linear equations and give their equations in the form y = ax+b. When given y = ax+b, plot the point (0,b), then plot a second point by adding (0,b) + (q,p), where slope = a = p/q. Then connect these points to create a unique line. Label the axes as x and y, and mark the relevant values along the axes. If not given y = ax+b, first solve the linear equation for y and simplify the result to obtain the form y = ax+b. Note: #10 does not have a y, so you can leave it in its current form.



1) y = x

2) y = -3x+6

3) y = 4x-7

4) x/5 + 3/2 = y

5) x-8 = 7-x-y

6) 5x+2y+5 = 3x-5+y



9) y = 4

10) x = 7



Given a graph with the following known information, find the unknown information [A]-[D]. Use slope = a = (y2-y1)/(x2-x1) when given 2 points. When given a point and a slope or a pair of points which doesn't included the y-intercept, plug in 1 point's x and y, as well as the value for a, and solve the equation for the unknown b. To find x-intercept, set y=0 and solve the resulting linear equation.

[A] y-intercept

[B] x-intercept

[C] slope

[D] equation of the line in form y = ax+b



1) Point: (0,1); Slope: 2

2) Point: (0,4); Slope: -3/2

3) Point: (1,-1); Slope: 3/4

4) Point: (-3,4); Point: (1,2)

5) Point: (0,0); Point: (3,0)

Answer 1

1)

 

Your first point to plot is the y-intercept (0, b).  Then, you will use the slope and y-intercept to find your second point.

 

a = p/q

 

 

From the y-intercept, move the point q units to the right.  Then move p units up (if slope is positive) or p units down (if slope is negative).  So your second point will be  (0 + q , b + p) if slope is positive or (0 + q , b - p) if slope is negative. Connect the two points.

 

Note: for some equations, you will need to convert to   y=ax+b  form.  In other words, solve for y.

 

 

 

2)

 

 

Use the point-slope form of a line to find your equation.

 

y = mx - mx₁ + y₁

 

where:
m = slope

(x₁ , y₁) is the given point