For each line, (a) find the slope and (b) sketch the graph. See E...

Question

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 2y = -3x

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the slope for the given line and plot it on the rectangular coordinate system. Our given line is eight Y equals negative 15 X. Well, our line is very close to being given in the format of our slope intercept form of a line which is Y equals M X plus B. We recall from previous lessons that M is our slope and that B is our Y intercept. And so we just need to solve for Y. Here, we can do that by dividing both sides of our equation by the eight. That's being multiplied by the Y which will simplify to Y equals a negative 15 8th X. So here we can identify our slope. That's what's being multiplied by the X. Our slope here is negative 15 8th. How about our Y intercept our B? Well, that's what's being added to the X and nothing's being added to the X. So the Y intercept is zero. It's at the origin, which is helpful for the graphing part of this. Now, for our graph, we can draw our rectangular coordinate system, we draw a vertical Y axis and a horizontal X axis, they come together at the origin in the middle. And now for our line, it's going through 00 through the origin. And then for the next point, well, we have our slope of negative 15 8th and we recall from previous lessons that that can colloquial colloquial Lee be known as rise over run. So the rise, that's the changes in the Y values divided by the run, That's the changes in the X values. So our rise here, the changes in Y are negative 15, that means it's going down 15 units. And then our run is the changes in X that's a positive eight. So it's going to the right eight units, eight positive X values. So on our rectangular coordinate system, we can denote where negative 15 would be. And the Y axis below the origin, you can also draw where positive 15 would be above the origin. On the Y axis. We can show where positive 15 would be on the X axis to the right of the origin and where negative 15 would be on the X axis to the left of the origin. Now from the origin, we are going down 15 units for the Y values. And then we're going to the right eight units for our X values which puts us approximately here. That's our point eight, negative 15. And to draw a line, we only need two points, we can connect these two points drawing a line straight through and going beyond. And because it's a negative slope as the X values head toward positive infinity, the Y values head toward negative infinity. And likewise, as our Y values head toward positive infinity, the X values head toward negative infinity. And that's our graph. Well done. We'll catch you on the next one.

For each line, (a) find the slope and (b) sketch the graph. See Examples 6 and 7. 2y = -3x

Key Concepts

Slope

Graphing Linear Equations

Standard Form of a Linear Equation

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