Solving Linear Equations
An equation is a mathematical statement that shows that two expressions are equal.
A linear equation is an equation in which the highest power of the variable is 1.
The goal of solving linear equations is to find the value of the variable that
makes the equation true.
To solve a linear equation, use inverse operations (adding, subtracting,
multiplying, or dividing) to isolate the variable on one side of the equation.
When solving equations, always check your answer by plugging it back into the
original equation.
Example: Solve for x: 3x + 5 = 14
Solution:
3x + 5 = 14 // Subtract 5 from both sides
3x = 9 // Divide both sides by 3
x = 3
Check: 3(3) + 5 = 14, so x = 3 is the correct solution.
Graphing Linear Equations
A linear equation can be graphed as a straight line on a coordinate plane.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope
and b is the y-intercept.
The slope of a line is the ratio of the vertical change (rise) to the horizontal
change (run) between any two points on the line.
The y-intercept of a line is the point where the line crosses the y-axis.
To graph a line using slope-intercept form, plot the y-intercept and use the slope
to find other points on the line.
Example: Graph the line y = 2x + 3.
Solution:
The y-intercept is (0,3).
The slope is 2, which means that for every 1 unit to the right, the line goes up 2
units.
Plot the y-intercept (0,3), then use the slope to find other points. For example,
if you move 1 unit to the right, you go up 2 units to (1,5). If you move 2 units to
the right, you go up 4 units to (2,7). Connect the points to graph the line.
An equation is a mathematical statement that shows that two expressions are equal.
A linear equation is an equation in which the highest power of the variable is 1.
The goal of solving linear equations is to find the value of the variable that
makes the equation true.
To solve a linear equation, use inverse operations (adding, subtracting,
multiplying, or dividing) to isolate the variable on one side of the equation.
When solving equations, always check your answer by plugging it back into the
original equation.
Example: Solve for x: 3x + 5 = 14
Solution:
3x + 5 = 14 // Subtract 5 from both sides
3x = 9 // Divide both sides by 3
x = 3
Check: 3(3) + 5 = 14, so x = 3 is the correct solution.
Graphing Linear Equations
A linear equation can be graphed as a straight line on a coordinate plane.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope
and b is the y-intercept.
The slope of a line is the ratio of the vertical change (rise) to the horizontal
change (run) between any two points on the line.
The y-intercept of a line is the point where the line crosses the y-axis.
To graph a line using slope-intercept form, plot the y-intercept and use the slope
to find other points on the line.
Example: Graph the line y = 2x + 3.
Solution:
The y-intercept is (0,3).
The slope is 2, which means that for every 1 unit to the right, the line goes up 2
units.
Plot the y-intercept (0,3), then use the slope to find other points. For example,
if you move 1 unit to the right, you go up 2 units to (1,5). If you move 2 units to
the right, you go up 4 units to (2,7). Connect the points to graph the line.
