Linear Equations

Linear equations serve as the bedrock of mathematical understanding, illustrating a direct line when plotted on a graph. Adhering to the structure y = mx + c, 'm' stands for the gradient or slope of the line, while 'c' signifies the y-intercept, and x and y are the variables. These equations are widely applied in diverse areas such as physics, engineering, and the field of economics.

Determining if Linear

Determine if the equation \(3x - 5y = 7\) is linear.
More examples

Solving Linear Equations

Solve the following linear equation for \(x\): \(3x - 5 = 4x + 7\)
More examples

Calculating Slope and y-Intercept

Find the slope and y-intercept of the line represented by the equation 2x + 3y = 6.
More examples

Rewriting in Slope-Intercept Form

Rewrite the equation 5x - 3y = 15 in slope-intercept form (y = mx + b).
More examples

Rewriting in Standard Form

Rewrite the linear equation \(3x - 2y = 6\) in standard form.
More examples

Finding x and y Intercepts

Find the x and y intercepts of the linear equation 2x - 3y = 6
More examples

Finding Equations Using the Slope-Intercept Formula

Find the equation of a line that passes through the point \((2,3)\) and has a slope of \(4\).
More examples

Finding Equations Using the Point Slope Formula

Find the equation of the line that passes through the point (2,3) and has a slope of -1.
More examples

Finding Equations Given Point and y-Intercept

Find the equation of the line that passes through the point (4, -2) and has a y-intercept of 3.
More examples

Finding the Constant Using Slope

Given a linear equation in the form y = mx + c, where m is the slope and c is the constant. If a line passes through the points (3,5) and (2,4) with a slope of 1, find the value of the constant c.
More examples

Finding Equations Using Two Points

Find the equation of the line that passes through the points (2, 3) and (4, 7).
More examples

Finding the Slope

Find the slope of the line that passes through the points (2, 3) and (4, 7).
More examples

Finding a Parallel Line Containing a Given Point

What is the equation of the line parallel to the line \(3x-4y+7=0\) and passing through the point (2, -3)?
More examples

Finding the Slope of a Parallel Line

Given the equation of a line as \(3x - 4y = 8\), find the slope of a line parallel to this line.
More examples

Finding the Slope of a Perpendicular Line

Given the linear equation \(3x - 4y = 7\), find the slope of the line perpendicular to it.
More examples

Finding a Perpendicular Line to the Given Line

Find the equation of the line that is perpendicular to the line \(3x - 2y = 5\) and passes through the point \((1, 2)\).
More examples

Finding Ordered Pair Solutions

Find the ordered pair solution for the following linear equation: 3x - 2y = 6
More examples

Using a Table of Values to Graph an Equation

Given the linear equation \(y = 2x + 3\), generate a table of values and use it to graph the equation.
More examples

Finding the Equation Using Point-Slope Form

Find the equation of the line that passes through the point (3,5) and has a slope of 2.
More examples

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More