Understanding linear equations in slope-intercept form and graphing y = -2/5x + 7

y = -2/5x + 7

The equation y = -2/5x + 7 represents a linear equation in slope-intercept form

The equation y = -2/5x + 7 represents a linear equation in slope-intercept form. In this form, the equation gives you information about the slope and y-intercept of the line.

The slope is the coefficient of the x-term, which in this case is -2/5. This means that for every increase of 1 in x, the y-value decreases by 2/5. Since the slope is negative, it tells us that the line is decreasing as we move from left to right.

The y-intercept is the constant term, which is 7 in this equation. It represents the y-coordinate where the line intersects the y-axis. So, when x = 0, y = 7.

To graph this equation, you can start by plotting the y-intercept, which is the point (0, 7). From there, you can use the slope to find additional points on the line. For example, if you move one unit to the right (from x = 0 to x = 1), you would move 2/5 units downwards. So, another point on the line would be (1, 7 – 2/5), which simplifies to (1, 6 3/5).

You can continue this process to find more points and then connect them to draw the line. Alternatively, you can use the slope-intercept form to find the y-coordinate for any given x-coordinate. For example, if you want to find the y-coordinate when x = 5, you can substitute x = 5 into the equation and solve for y:

y = -2/5(5) + 7
y = -10/5 + 7
y = -2 + 7
y = 5

So, when x = 5, y = 5, and you can plot the point (5, 5) on the graph.

Once you have a few points, you can connect them with a straight line to represent the graph of the equation.

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