Write an equation in point-slope form and general form of the line passing through (-5,3) and pe

Write an equation in point-slope form and general form of...

Key Concepts

Point-Slope Form

Point-slope form is an equation format for lines that emphasizes a given point and the slope of the line. It is written as y - y? = m(x - x?), where (x?, y?) is a specific point on the line and m represents the slope. This form is especially useful when you know one point through which the line passes and the slope of the line.

General Form of a Linear Equation

The general form of a linear equation is written as Ax + By + C = 0, where A, B, and C are constants. This format provides a standardized way to represent lines, making it easier to compare different linear equations, analyze intersections, and solve systems of equations.

Slope of a Line

The slope of a line quantifies its steepness and direction by describing the ratio of the vertical change to the horizontal change between any two points on the line. It is a fundamental concept in analytic geometry and is essential for understanding and constructing linear equations.

Perpendicular Slopes

In coordinate geometry, two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope m, then the perpendicular line will have a slope of -1/m. This negative reciprocal relationship is key when finding the equation of a line that must be perpendicular to a given line.

Transcript

00:01 This problem is a review problem from past stuff that you guys have learned.

00:05 Right off the bat tells us we are eventually going to be trying to write an equation in point slope form.

00:10 So that would imply that you need to know point slope form.

00:13 Point slope form is y minus y sub 1 equals m times x minus x sub 1.

00:21 And remember that m represents slope, by the way.

00:24 Meaning we have an x1 and a y1 which is a place for an x and y coordinate to be plugged in and then we have m which is a place for us to plug in the slope well we already know that this equation is supposed to be passing through the point negative 5 3 remember all coordinate points are given to us in x comma y form meaning i already know 3 is the y value that i'm going to be plugging in and we know that we know that that negative 5 is the x value that we're going to be plugging in.

00:59 Meaning that's how our point slope form looks right now.

01:02 The only question we have left is what is our slope? well, we aren't given the slope right off the bat.

01:09 Instead, to make things a little tougher on us, what they have done is they have given us another line, an equation for another line that i've written right here.

01:19 And what they've told us is the equation of this line has a slope that is perpendicular.

01:24 To the line we want to find.

01:27 I'll say that again, because this is the part that can be kind of confusing with these questions.

01:31 We are being given a random equation here.

01:34 This line does not represent the actual answer.

01:38 This is a random equation of a line.

01:41 But what they have told us is that if we can find the slope of this equation, if we can find the slope of this equation, if we can then find a slope perpendicular to it, that's what we want over here.

01:59 The answer that we are trying to find will be using a slope perpendicular to this equation.

02:06 So, first things first, let's actually find the slope of this equation.

02:12 Remember the way, the easiest way i would say to find the slope of this equation is to put this equation in slope intercept form, meaning y equals mx plus b or in other words we need to solve this equation out for y so i've got 5y it is a positive 5y so i'm going to keep it on that side i'm going to subtract x and add 7 to the other side to get them away from the y okay so i'd have 5y equals negative x plus 7 to get y completely by itself i need to divide by 5 that does mean i have to divide everything by 5, which means i do have a negative 1 fifth x.

02:57 Remember there was a negative 1 in front of this, right? and i also have plus 7 fifths.

03:04 Now that's a nasty looking problem.

03:06 However, it really doesn't matter because i don't even care about the 7 fifths...

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