Write an equation for each line. Then graph the line. through (-3,-1) and perpendicular to y=-(2

step 1 So we want to find an equation for this line. It goes through the point negative 3, negative 1,

Write an equation for each line. Then graph the line....

Key Concepts

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation and drawing a straight line through them. Understanding the slope and y-intercept (or other forms like point-slope) allows one to accurately represent the line on a coordinate grid, making it easier to visualize linear relationships and intersections.

Slope

The slope is a measure of the steepness of a line, defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is a fundamental concept in coordinate geometry and is essential for understanding the behavior of linear functions and their graphs.

Perpendicular Lines

Two lines are perpendicular if the product of their slopes is -1, meaning their slopes are negative reciprocals of each other. This relationship is crucial when constructing or identifying a line that intersects another at a right angle, allowing for precise determination of the new line’s slope.

Point-Slope Form

The point-slope form of a line provides a method to write the equation of a line when a point on the line and its slope are known. It is expressed as y - y? = m(x - x?), where (x?, y?) is a point on the line and m is the slope. This form is particularly useful for quickly formulating a line’s equation before converting it to another format if needed.

Transcript

00:01 So we want to find an equation for this line.

00:03 It goes through the point negative 3, negative 1, and it's perpendicular to this line here.

00:11 So whenever we see the word perpendicular, we want to take the slope and take the negative reciprocal of it.

00:21 So the slope is negative 2 fits.

00:25 But if it's perpendicular, our slope is now positive 5 over 2, because we just take the negative reciprocal.

00:38 So you just flip the top and the bottom on that fraction.

00:44 So this is our new slope.

00:46 But we need to write a line that goes through these points here.

00:51 So let's say this is x1 and this is y1.

00:54 So since we have a point in a slope, we can use point slope form.

01:03 So this is y minus y1 equals m times x minus x1.

01:09 So this becomes y minus negative 1 equals 5 over 2 times xx minus negative 3.

01:18 This becomes y plus 1, say equal to 5 over 2 times x plus 3 as our line.

01:32 So they also want us to graph.

01:35 So we had y plus 1 equals 5 over 2 times x plus 3.

01:47 The easiest way to graph this is to first get y by itself and write it in that form.

01:52 So we'll have y plus 1 equals.

01:55 Is 5 over 2 x plus 15 over 2 and then just subtract one from both sides so we'll have 5 over 2 x plus 13 over 2.

02:12 So if we draw a graph and we also want to start at our y intercept...

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