Mathematics

Question

1.) (-4,-3); m=2/3
given point, then graph a line with the given slope

1 Answer

  • Answer:

    To graph a line with a given slope, we can use the point-slope form of a linear equation, which is given by the formula y - y1 = m(x - x1). In this formula, (x1, y1) is the given point and m is the slope of the line.

    Substituting the given values into the point-slope formula, we have:

    y - (-3) = (2/3)(x - (-4))

    Solving for y, we have:

    y = (2/3)x + (5/3)

    This is the equation of the line in slope-intercept form. To graph the line, we can plot the given point (-4, -3) and then use the slope (2/3) to find additional points on the line. For example, if we let x = -3, we have:

    y = (2/3)(-3) + (5/3) = -2 + 5/3 = 1/3

    So, another point on the line is (-3, 1/3). We can repeat this process to find additional points on the line.

    The graph of the line would then be a set of points that includes (-4, -3) and (-3, 1/3), as well as all other points that can be found using the point-slope formula.

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