Question Video: Finding in Point-Slope Form the Equation of a Line | Nagwa Question Video: Finding in Point-Slope Form the Equation of a Line | Nagwa

# Question Video: Finding in Point-Slope Form the Equation of a Line Mathematics

Find, in point-slope form, the equation of the line with slope 2/7 that passes through the point π΄ (1, β10).

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### Video Transcript

Find, in point slope form, the equation of the line with slope two-sevenths that passes through the point π΄: one, negative 10.

In order to work out the equation of a line, we need to use the formula π¦ minus π¦ one equals π brackets or parentheses π₯ minus π₯ one, where π is the gradient or the slope of the line and π₯ one and π¦ one are the ordered pair or coordinate that the line passes through.

Substituting in the numbers into the equation gives us π¦ minus negative 10 equals two-sevenths multiplied by π₯ 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 π¦ plus 10 equals two-sevenths multiplied by π₯ minus one. This is the equation of the line with slope two-sevenths that passes through the point one, negative 10.

In some cases, weβll be asked to simplify this equation or remove the fractions from the equation, so we only have integer or whole numbers. Letβs assume we wanted to simplify this equation to leave our answer with only integer values. Letβs first multiply both sides of our equation by seven. This leaves us on the left-hand side with seven multiplied by π¦ plus 10 and on the right-hand side with two multiplied by π₯ minus one.

Expanding or multiplying out the parentheses or brackets gives us seven π¦ plus 70 and on the right-hand side two π₯ minus two. Our next step is to subtract 70 from both sides of the equation, giving us seven π¦ equals two π₯ minus two minus 70, leaving us with a final answer of seven π¦ equals two π₯ minus 72.

The coefficients or numbers in front of π₯ and π¦ are now integers or whole numbers, so an alternative equation to π¦ plus 10 equals two-sevenths multiplied by π₯ minus one is seven π¦ equals two π₯ minus 72.

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