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5. Graph a line with a slope of 2 and goes through the point (-1,3)

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MerylMaster · Tutor for 5 years

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To graph a line with a given slope and through a specific point, we can use the point-slope form of the equation of a line. The point-slope form is given by:\[y - y_1 = m(x - x_1)\]where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through.Given the slope \(m = 2\) and the point \((-1, 3)\), we can substitute these values into the point-slope form:\[y - y_1 = m(x - x_1)\]\[y - 3 = 2(x - (-1))\]\[y - 3 = 2(x + 1)\]Now, let's simplify the equation:\[y - 3 = 2x + 2\]To graph this line, we can follow these steps:1. Plot the given point \((-1, 3)\) on the graph.2. Use the slope to find another point. Since the slope is 2, it means that for every 1 unit we move to the right (positive x-direction), we move 2 units up (positive y-direction). Starting from the point \((-1, 3)\), if we move 1 unit to the right, we will be at \((-1 + 1, 3 + 2) = (0, 5)\). Plot this second point.3. Draw a line through the two points, extending it in both directions.The equation of the line in slope-intercept form (if needed) can be found by solving for \(y\):\[y = 2x + 5\]This is the equation of the line in slope-intercept form, where the y-intercept is \((0, 5)\).The accurate answer for the equation of the line in point-slope form is \(y - 3 = 2(x + 1)\), and in slope-intercept form, it is \(y = 2x + 5\).

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5. Graph a line with a slope of 2 and goes through the point (-1,3)

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