Graph the line represented by the equation y = − 4 5 x + 2 y=-\frac45x+2 .

this problem we are asked to graph the line represented by the equation y equals negative four fifths x plus two, and here we have this graph that we can work with. So how do I go about solving this problem? Well, what I can recognize is slope intercept form, y equals m x plus b. This tells me my slope and my y intercept. Now I can clearly see that my slope is going to correspond to this negative four fifths right here. Now negative four fifths is the slope, which I'm also gonna write like this, negative four over five. And the reason I'm writing it like this, where I just move this negative sign to the four, is because I know that the slope is the rise over the run. And that's going to help us when it comes to graphing things. So we have now found our slope. So now that we have our slope, the next thing I need is my y intercept. My y intercept, I can see, happens at two. So because we're adding on this two, that means b equals two. Now what can I do with this information? Well, what I can see is that the y intercept happens at two, so that means if I go on to y here, the line is going to cross at two. But now I need to figure out what this line is going to look like, what its slant is gonna be. I obviously can't just draw a random line through here because we don't know which direction or how this line is going to be slanted. So that's what the slope here is going to tell me. The rise is negative four. The run is five. So what that means is going over to this point, I can rise negative four, which means since it's negative, I'm going to be going down. So we're gonna go down one, two, three, four. So that's where my rise is gonna be, and then my run is five. So we're gonna go one, two, three, four, five. And so there's our point right there. So notice here we now have two points, which means we can connect these with a line. So if I draw a line through these two points like so, this is gonna give me the equation of my line and or this is gonna give me the line on my graph. And you wanna make sure to line these up very carefully just so it goes through both points. That looks pretty accurate right there. So this is gonna be my line, and that would be the solution to this problem. So this is how you can graph the line given the equation in slope intercept form. Hope you found this helpful, and let's move on.

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Graph the line represented by the equation $y = - \frac{4}{5} x + 2$ .

Graph of the line y = -4/5 x + 2 with plotted points at (0,2) and (5,-2) on a labeled coordinate plane.

Graph of the line y = -4/5 x + 2 with points at (0,2) and (-5,6) on a labeled xy-coordinate plane.

Graph of the line y = -4/5 x + 2 with points at (0,2) and (5,-2) on a labeled coordinate plane.

Graph of the line y = -4/5 x + 2 with plotted points and a downward sloping purple line on a grid.

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Identify the equation of the line given: $y = -\frac{4}{5}x + 2$. This is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Locate the y-intercept $b = 2$ on the graph. This is the point where the line crosses the y-axis, so plot the point $(0, 2)$.

Use the slope $m = -\frac{4}{5}$ to find another point. The slope means that for every 5 units you move to the right (positive direction on the x-axis), you move 4 units down (negative direction on the y-axis). Starting from $(0, 2)$, move right 5 units to $x=5$ and down 4 units to $y = 2 - 4 = -2$, so plot the point $(5, -2)$.

Draw a straight line through the points $(0, 2)$ and $(5, -2)$ extending in both directions. This line represents the graph of the equation.

Verify the line by checking if other points satisfy the equation or lie on the line, ensuring the slope and intercept are correctly represented.