HOW TO GRAPH LINEAR EQUATIONS IN
SLOPE INTERCEPT FORM
Linear equation in slope-intercept form :
y = mx + b
Here, m stands for slope and b stands for y-intercept.
We already know that the graph any linear equation will be a straight line.
When we have a linear equation in slope-intercept form, we can sketch the
graph (straight line) of the equation using the slope 'm' and y-intercept 'b'.
y-intercept :
y-intercept is nothing but the value at where the line intersects y-axis.
Slope :
Slope is sometimes referred to as "rise over run".
That is,
slope = rise/run
Because the fraction consists of the rise (the change in y, going up or down)
divided by the run (the change in x, going from left to the right).
Rising/Falling/Horizontal/Vertical Line :
(i) If the slope of a line is positive, then the line will be going (from left to
right) up and it is called rising line.
,(ii) If the slope of a line is positive, then the line will be going (from left to
right) down and it is called falling line.
(iii) If the slope is zero, the line will be horizontal.
(iv) If the slope is undefined, the line will be vertical.
Graph each of the following linear equations :
Example 1 :
y = (¼)x - 1
, Solution :
The given linear equation is in slope-intercept form.
Comparing y = mx + b and y = (¼)x - 1,
slope m = ¼
y-intercept b = -1
Since slope (¼) is a positive value, the line is a rising line.
rise/run = ¼
rise = 1
run = 4
Since the y-intercept is -1, the line intersects y-axis at -1.
Graphing :
Step 1 :
Plot the y-intercept at (0, -1).
Step 2 :
Since the rise (1) is a positive value, move 1 unit up from the y-intercept (0, -
1).
Step 3 :
Since the run is 4, move 4 units to the right from the position reached in
step 2.
SLOPE INTERCEPT FORM
Linear equation in slope-intercept form :
y = mx + b
Here, m stands for slope and b stands for y-intercept.
We already know that the graph any linear equation will be a straight line.
When we have a linear equation in slope-intercept form, we can sketch the
graph (straight line) of the equation using the slope 'm' and y-intercept 'b'.
y-intercept :
y-intercept is nothing but the value at where the line intersects y-axis.
Slope :
Slope is sometimes referred to as "rise over run".
That is,
slope = rise/run
Because the fraction consists of the rise (the change in y, going up or down)
divided by the run (the change in x, going from left to the right).
Rising/Falling/Horizontal/Vertical Line :
(i) If the slope of a line is positive, then the line will be going (from left to
right) up and it is called rising line.
,(ii) If the slope of a line is positive, then the line will be going (from left to
right) down and it is called falling line.
(iii) If the slope is zero, the line will be horizontal.
(iv) If the slope is undefined, the line will be vertical.
Graph each of the following linear equations :
Example 1 :
y = (¼)x - 1
, Solution :
The given linear equation is in slope-intercept form.
Comparing y = mx + b and y = (¼)x - 1,
slope m = ¼
y-intercept b = -1
Since slope (¼) is a positive value, the line is a rising line.
rise/run = ¼
rise = 1
run = 4
Since the y-intercept is -1, the line intersects y-axis at -1.
Graphing :
Step 1 :
Plot the y-intercept at (0, -1).
Step 2 :
Since the rise (1) is a positive value, move 1 unit up from the y-intercept (0, -
1).
Step 3 :
Since the run is 4, move 4 units to the right from the position reached in
step 2.
