Question Video: Finding the Equation of a Straight Line | Nagwa Question Video: Finding the Equation of a Straight Line | Nagwa

# Question Video: Finding the Equation of a Straight Line Mathematics • Third Year of Preparatory School

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Determine the equation of the line passing through π΄ (0, 16) and π΅ (1, β9) in slope-intercept form.

02:59

### Video Transcript

Determine the equation of the line passing through π΄: zero, 16 and π΅: one, negative nine in slope-intercept form.

So in this question, weβre given the coordinates of two points that lie on a straight line, and weβre asked to determine its equation. Weβve also been asked for the equation in a specific form, slope-intercept form. This is π¦ equals ππ₯ plus π, where π represents the slope of the line and π represents the π¦-intercept. In order to answer this question, we need to determine both of these values, the slope and the π¦-intercept.

So letβs look carefully at the information in the question and the coordinates of the two points weβve been given that lie on the line. The first of these two points, π΄, has coordinates zero, 16. As the π₯-coordinate of this point is zero, this is a point on the π¦-axis. And therefore, these are the coordinates of the π¦-intercept. The π¦-coordinate is 16 and this tells us the value of π in our equation is also 16. So we can substitute this value of π into the equation of our line. So we have that π¦ equals ππ₯ plus 16 for a value of π that we now need to calculate.

Remember, π represents the slope of the line. If we know the coordinates of two points on the line β which weβll refer to as π₯ one, π¦ one and π₯ two, π¦ two β then the slope can be calculated using this formula: π is equal to π¦ two minus π¦ one over π₯ two minus π₯ one. It doesnβt matter which of the two points we think of as π₯ one, π¦ one and which we think of as π₯ two, π¦ two. Iβm going to choose to subtract the coordinates of point π΄ from those of point π΅.

So letβs calculate the slope of this line. π is equal to π¦ two minus π¦ one, so that is negative nine minus 16. And then I need to divide by π₯ two minus π₯ one, so thatβs one minus zero. My calculation for the slope simplifies to negative 25 over one, and of course thatβs just equal to negative 25. The final step in answering this question is I need to substitute this calculated value of π into the equation of the line.

So in doing so, I have that π¦ is equal to negative 25π₯ plus 16. And thatβs our answer to this problem, the equation of the line in slope-intercept form.

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