Question Video: Finding in Slope-Intercept Form the Equation of Parallel Lines | Nagwa Question Video: Finding in Slope-Intercept Form the Equation of Parallel Lines | Nagwa

# Question Video: Finding in Slope-Intercept Form the Equation of Parallel Lines Mathematics • Third Year of Preparatory School

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Find, in slope-intercept form, the equation of a line parallel to π¦ = β(8/3)π₯ + 3 that passes through point π΄(β3, 2).

02:42

### Video Transcript

Find, in slope-intercept form, the equation of a line parallel to π¦ equals negative eight-thirds π₯ plus three, that passes through point π΄: negative three, two.

To solve this problem, we can use the point slope formula. The point slope formula says π¦ minus π equals π times π₯ minus π, where π equals the slope and π, π is the given point.

In our problem, weβve been given both, the point and the slope. You might be curious what the slope is since our question doesnβt explicitly say the slope. Thatβs okay because our question tells us that the line is parallel to π¦ equals negative eight-thirds π₯ plus three. And we know that parallel lines have the same slope. The slope of the line π¦ equals negative eight-thirds π₯ plus three is negative eight-thirds. And since parallel lines have the same slope, the slope of our line is also negative eight-thirds.

We have a slope. Now we also have a point, negative three, two. Letβs plug everything in. Plug in two for π, so π¦ minus two equals negative eight-thirds, plugged in for π, times π₯ minus negative three. Negative three, itβs been plugged in for π.

Now we can simplify this equation. Weβll say that π₯ minus negative three equals π₯ plus three. Then we need to distribute our negative eight-thirds, to π₯ and three. Negative eight-thirds times π₯ equals negative eight-thirds π₯. Negative eight-thirds times three equals negative eight.

Weβre nearly there with our slope intercept form. But for slope intercept form, we need π¦ by itself. To do that, we add two to both sides of our equation. On the left, weβre left with π¦ and on the right, negative eight-thirds π₯ minus six.

The equation of a line parallel to π¦ equals negative eight-thirds π₯ plus three β that also passes through point negative three, two β equals negative eight-thirds π₯ minus six.

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