![]() ![]() And you don't have to draw it to do this problem but it always help to visualize That is my y axis. What is the equation of the line? Let's just try to visualize this. This means that it is an ENTIRELY different point on the line, as the change in y over change in x is equal to -10/6, or -5/3.Ī line goes through the points (-1, 6) and (5, -4). 69/15 = x And lastly, dividing -69 by 15 gives us.Īlright, so we know that when y is equal to -10, then x is equal to -4.6. 23/3 * 3/5 = x And multiplying this out will give us. 23/3 / 5/3 = x As for the left hand side, we know that dividing by a fraction is the same thing as multiplying by it's reciprocal, so it becomes 23/3 / 5/3 = 5/3x / 5/3 The right hand side cancels out 23/3 = 5/3x, so now we divide both sides by 5/3 So first, we subtract 13/3 from both sides. 10 = 5/3x + 13/3 and from this, we can solve for x in this situation. Now to compare this to when y equal to -10, we would have this: We also know from the given points that when y equals 6, x is equal to -1. The change in y over the change in x equals out to -10/6, or -5/3. This is seen when you compare the points and the slope. However if Sal were to use -10, the x value he would have to be different. If -10 from the slope were to be a valid option for a point in this equation, that means that the change in x would also have to be the accompanying point on the line to go with the change in y. He could not use -10, because -10 isn't necessarily a point on the line, because it's the change in y. Students can also rearrange the equation to be in slope intercept form to avoid confusion, y=3 x+10.He used 6 because it was one of the points for y on the line. The coefficient of x is 3 which means the slope is 3.Īlso, when x = 0, \, y=10+3(0), the value of y is 10 which means the y -intercept is 10. Since the equation is not quite in slope-intercept form, y=m x+b, students might think that the slope is 10 because it is written first and that the y -intercept is 3. Rearrange the equation to make sure it is in the form of \textbf -interceptįor example, the equation y=10+3 x.State the slope and y -intercept of the line y=-3 x+8. High School Functions: Linear, Quadratic, and Exponential Models (HSF-LE.A.2):Ĭonstruct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).Graph linear and quadratic functions and show intercepts, maxima, and minima. High School Functions: Interpreting Functions (HSF-IF.C.7a):.Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane derive the equation y = m x for a line through the origin and the equation y = m x + b for a line intercepting the vertical axis at b. Grade 8 Expressions and Equations (8.EE.B.6).For example, the function A=s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2, 4) and (3,9), which are not on a straight line. Interpret the equation y=m x+b as defining a linear function, whose graph is a straight line give examples of functions that are not linear. How does this relate to 8 th grade math and high school math? Graphically, you can see that the ordered pair of the y -intercept is (0, 1) and the slope is represented by 2 units up and 1 unit to the right. You can state that the slope of this line is 2 and the y -intercept is 1. Since m is represented by the number 2 and b is represented by the number 1. ![]() Let’s take a look at the linear equation y=2 x+1. You can also determine this because the power of x is equal to 1. ![]() Y=m x+b is a linear equation because when it’s graphed on the coordinate plane, it forms a line.
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