Mathematics, 08.01.2020 08:31 squawk1738

Which graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2/3x – 2?

Which graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2

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Answer from: melanieambrosy

Graph 4

Step-by-step explanation:

When being asked problems like this one, even before working out any specifics, looking at the direction the line is moving in, you can at least eliminate some answers. When a graph has a negative slope, it will be decreasing as it moves to the right on the x-axis (its direction will look somewhat like a \, but not always this steep). Only two answers to this question have these properties, Graph 3 and Graph 4. Because of this trick, we're able to eliminate Graph 1 and Graph 2 as possible answers to this question, but how do we decide between Graph 3 and Graph 4? This is where knowledge on Linear Equations come into play.

is the parent function for linear equations, and its properties are as follows:

is the equation's slope; determining the magnitude and direction of a linear line. Slope represents a ratio of how many units a function moves up or down to how much it moves left or right. For example, the equation $y=\frac{2}{3}x$ has a slope of $\frac{2}{3}$ . If the numerator of the function,

, represents how far the function moves upwards, and the denominator of the function,

, represents its movement to the right, then for every 2 units the function goes upwards, that's 3 units to the right. If there were negative values in the slope (ex: $-\frac{2}{3}$ ), then one of the directions would be down, or left.

represents the linear function's y-intercept; the y value it hits on the y-axis. For example, the equation y=x+1

will hit the y axis at the point (0,1). This will help us finish solving the equation.

Looking at the two remaining graphs and using our knowledge on , we can see that Graph 3 hits the y-axis above and Graph 4 hits the y-axis below . If this problem is asking for the graph to have the same y-intercept as $y=\frac{2}{3}x-2$ , then with being , we can figure that the function we want to make will have to hit the y-axis at , below . Only Graph 4 has these properties, so it is the answer.

Answer from: Quest

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step-by-step explanation:

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3.how is solving radical equations different than solving linear equations?

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Which graph represents a line with a slope of -2/3 and a y-intercept equal to that of the line y = 2...