Forms of linear equations: FAQ

There are countless applications for linear equations in the real world! For example, engineers might use linear equations to study the relationships between different physical properties, like force and displacement. Economists might use linear equations to model supply and demand, or to predict future trends.

Practice with our Linear equations word problems exercise.

Slope-intercept form is one way to write a linear equation. The form is $y = mx + b$y, equals, m, x, plus, b, where $m$m is the slope of the line and $b$b is the $y$y-intercept.

Practice with our Slope-intercept intro exercise.

Start by finding the $y$y-intercept, or the point where the line crosses the $y$y-axis. Plot that point first. Then, use the slope to find other points on the line. Remember that slope is "rise over run" - if the slope is positive, the line will go up as it goes to the right, and if the slope is negative, the line will go down as it goes to the right.

Practice with our Graph from slope-intercept form exercise.

We need two pieces of information: the slope and the $y$y-intercept. Once we have those, we substitute the values in for $m$m and $b$b in the equation $y = mx + b$y, equals, m, x, plus, b.

Practice with our Slope-intercept equation from graph exercise.

Point-slope form is another way to write a linear equation. The form is $y - y_1 = m(x - x_1)$y, minus, y, start subscript, 1, end subscript, equals, m, left parenthesis, x, minus, x, start subscript, 1, end subscript, right parenthesis, where $m$m is the slope and $(x_1, y_1)$left parenthesis, x, start subscript, 1, end subscript, comma, y, start subscript, 1, end subscript, right parenthesis is any point on the line.

Practice with our Point-slope form exercise.

Standard form is yet another way to write a linear equation. The form is $Ax + By = C$A, x, plus, B, y, equals, C, where $A$A, $B$B, and $C$C are constants.

Practice with our Graph from linear standard form exercise.

Practice with our Convert linear equations to standard form exercise.

There are a few reasons we might choose to rewrite a linear equation in a different form. For example, if we're trying to graph the equation, slope-intercept form might be the easiest to work with. But if we're trying to solve a system of equations, standard form might be more useful. It really depends on the situation.

Practice with our Linear equations in any form exercise.