Find, in point slope form, the equation of the line with slope two-sevenths that passes through the point 𝐴: one, negative 10.
In order to work out the equation of a line, we need to use the formula 𝑦 minus 𝑦 one equals 𝑚 brackets or parentheses 𝑥 minus 𝑥 one, where 𝑚 is the gradient or the slope of the line and 𝑥 one and 𝑦 one are the ordered pair or coordinate that the line passes through.
Substituting in the numbers into the equation gives us 𝑦 minus negative 10 equals two-sevenths multiplied by 𝑥 minus one. Subtracting a negative number becomes a positive, as we end up moving up our number line. We can therefore simplify the equation to 𝑦 plus 10 equals two-sevenths multiplied by 𝑥 minus one. This is the equation of the line with slope two-sevenths that passes through the point one, negative 10.
In some cases, we’ll be asked to simplify this equation or remove the fractions from the equation, so we only have integer or whole numbers. Let’s assume we wanted to simplify this equation to leave our answer with only integer values. Let’s first multiply both sides of our equation by seven. This leaves us on the left-hand side with seven multiplied by 𝑦 plus 10 and on the right-hand side with two multiplied by 𝑥 minus one.
Expanding or multiplying out the parentheses or brackets gives us seven 𝑦 plus 70 and on the right-hand side two 𝑥 minus two. Our next step is to subtract 70 from both sides of the equation, giving us seven 𝑦 equals two 𝑥 minus two minus 70, leaving us with a final answer of seven 𝑦 equals two 𝑥 minus 72.
The coefficients or numbers in front of 𝑥 and 𝑦 are now integers or whole numbers, so an alternative equation to 𝑦 plus 10 equals two-sevenths multiplied by 𝑥 minus one is seven 𝑦 equals two 𝑥 minus 72.