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Math Asked by a SnapAndSolve user · 21 minutes ago

The slope of a line is -3, and a point on the line is (4, -1). Can the equation of the line be expressed in...

1. The slope of a line is -3, and a point on the line is (4, -1). Can the equation of the line be expressed in slope-intercept form? If so, what is the equation? Does the line pass through the origin? How do you know?
2. Is the graph of y = x^2 + 2 a straight line? Explain.

Answer

  1. Yes, the equation of the line can be expressed in slope-intercept form, which is y = mx + b. Given the slope (m) is -3 and a point (4, -1), we can use the point-slope form to find the y-intercept (b):

    y - (-1) = -3(x - 4)

    y + 1 = -3x + 12

    y = -3x + 11

    So, the equation is y = -3x + 11. The line does not pass through the origin (0,0) because substituting x = 0 gives y = 11, not 0.

  2. No, the graph of y = x^2 + 2 is not a straight line. It is a parabola because the equation is quadratic, with the highest power of x being 2.

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