Equations Of A Line

Standard Form:                                          Ax+By=C
Slope-Intercept Form:                         y=mx+b
Point -Slope Form:                                   y-y₁=m (x-x₁)

Standard Form

The standard form of a linear equation is Ax+By=C where A and B are not both zero. A quick way to graph an equation in standard form is to plot its intercepts. The y-intercept of a line is where the y-coordinate intersects the y-axis. If the equation of a line intersects the y-axis at the point (0,r) then the number "r" is the y-intercept. The x-intercept of a line is the x-coordinate of the point where the line intersects the x-axis. If the equation of a line intersects the x-axis at the point (g,0), then the number "g" is the x-intercept.

Graphing Equations In Standard Form

Step 1    Write the equation in standard form.
Step 2   Find the x-intercept by letting y=0 and solving for x. Use the x-intercept to plot the point where the line crosses the x-axis.
Step 3   Find the y-intercept by letting x=0 and solving for y. Use the y-intercept to plot the point where the line crosses the y-axis.
Step 4   Draw a line through the two points.

y=(3/2)x-1                                                     y=4x+1
2y=3x-1                                                           y-4x=1
2y-3x=-1                                                         - 4x+y=1
3x-2y=1                                                           4x-y=-1

Slope Intercept Form
Notice that when the slope, m, is positive, the line slants upward to the right. The more positive m is, the steeper the line will slant upward to the right.
When the slope is negative, the line slants downward to the right, and, as the slope becomes more and more negative, the line will slant downward steeper and steeper to the right.
Also, notice that when the y-intercept, b, is positive, the line crosses the y-axes above y = 0. When b is negative, the line crosses the y-axis somewhere below y = 0. In fact, b is the value on the y-axis where the line passes through this axis. The line intercepts, or crosses, the y-axis here, and, therefore, b is called the y-intercept.

Write the equation of a line with the given slope and y-intercept:
m=3, b=2 Answer: y=3x+2

As the name suggests we need a point on the line and the slope of the line to use this equation. We take as a general point on the line, as the point we know, and m as the slope.

Point-Slope Form

(y-y1) = m(x-x1)

y-y1 = mx - mx1 distributive property

y = mx - mx1 +y1 additive inverse (y1-y1=0) and adding the

same quantity to both sides (y1 in this case)

y = mx + (y1-mx1) commutative and associative properties of

addition

y = mx + b let b = (y1 - mx1)

You gave me the following point and slope: (1, 3), m = -2.

    y-3 = -2(x-1)
    y-3 = -2x+2
     y = -2x+2+3
     y = -2x+5

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